Well, I dunno. sounds like Fletcher made a significant contribution to the lyrics, but the finished product seems to be Porter's work. I'm repeating part of what Allan posted above, so the whole song is in proper order.
-Joe Offer-

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(from The Complete Lyrics of Cole Porter, Robert Kimball, 1983)

"Don't Fence Me In"
(Cole Porter & Bob Fletcher)

Published October 1944. After the triumphant launching of Anything Goes at the Colonial Theatre in Boston on November 5, 1934, Porter signed a contract with Twentieth Century Fox to provide songs for a film tentatively titled Adios, Argentina. The plot concerned the decision of an orphan girl who had inherited a big cattle spread in Texas to ship her four polo-playing cowboy tutors East to challenge the winner of a polo match between teams from the United States and Argentina. At one point the cowhands, unable to find anyone to accept their challenge, were supposed to burst into song to express their loneliness for the life back on the ranch. Hired presumably for his exceptional talent at writing songs with a distinct Latin flavor, Porter was also expected to write the cowboy song required by producer Lou Brock for this nostalgic moment in the film.

A month earlier Brock had received a book of verse from his friend Bob Fletcher, then employed in Helena, Montana, as Plans and Traffic Engineer for the Montana State Highway Department. In response, Brock wrote of the fancy he had taken to having a song entitled "Don't Fence Me In" in Adios, Argentina and added, "If I use this, will probably have you write or collaborate on the lyrics for the tune, in which event I would want the chorus to start with the words `Don't Fence Me In.'" Fletcher promptly wrote a song. On November 3, Brock wired Fletcher asking him to send a copy of the song care of the Waldorf-Astoria in New York, where Brock was staying in his ultimately successful quest to persuade Porter to write the score for the film. Porter signed with Fox on November 14. One week later, Brock asked Fletcher to send a copy of his song to Porter, whom he described as "one of our very best composers, who is rated as high as anyone on Broadway at the present time. Unlike most of the others, he also writes his own lyrics and does not as a rule have anyone collaborating with him. However, he was very much interested in your stuff, and what kind of a deal I can work out with him I do not know as these are matters to press somewhat delicately with a man of his standing."

On November 24, Fletcher sent Porter the lyrics and music for the refrain of "Don't Fence Me In" and some lyrics for a verse. On December 1, Brock wired Fletcher that "Cole Porter wants to buy right to use title and some characteristic words and phrases from your lyrics. Suggest you quote him price two hundred fifty dollars outright. Account Porter's reputation for always doing his own lyrics, believe impractical for him to give you credit. In any event, please wire him your proposition direct immediately and write me what you have done."

Fletcher complied with Brock's request, and Porter accepted the offer, perhaps for the simple reason that his producer had asked him to do so. Whether Porter was unable to write a satisfactory cowboy song is impossible to know. The primary center of musical-comedy production, however, had shifted from Broadway to Hollywood and the opportunities and money were incomparably greater at the Hollywood sound studios. Porter was hopeful that, should he prove to be a "cooperative" creator, the initial assignment from Fox would lead to more exciting and more lucrative offers from the film capital in the future.

The agreement, dated December 11 and signed by both Porter and Fletcher, gave Porter all of Fletcher's rights to the title and lyrics of "Don't Fence Me In" for the sum of $250. The agreement did not apply to Fletcher's music, which Porter did not use in any way. Porter also promised Fletcher that he would do all in his power to see that Fletcher received recognition for the material he sold to Porter.

On January 7, 1935, Porter, acknowledging Fletcher's Christmas gift of a book of his verse, sent Fletcher a copy of "Don't Fence Me In." Advising Fletcher "to keep it carefully under your hat as the music will not be released until next autumn," Porter also wrote, "I have given you credit under the title. Hope you will be pleased with it. Certainly, I am very grateful to you."

A week earlier Porter had gone to the Brunswick studios, where, with the assistance of baritone Edward Nell, pianist Victor Piemonte, and the Anything Goes Foursome Quartet, he had participated as a pianist in recording a complete set of demonstration discs of the six songs he had written for the film: "Adios, Argentina," "The Chinpah," "Don't Fence Me In," "If You Could Love Me," "The Side Car," and "Singing in the Saddle." The records were sent to Lou Brock at the Fox studio in Hollywood, but the picture was never filmed and the score went into the trunk.

Ten years later, "Don't Fence Me In" was pulled off the shelves of Harms, Inc., then owned by Warner Brothers, and used in Hollywood Canteen, where it was sung by Roy Rogers. A best-selling record by Bing Crosby and the Andrews Sisters sent it to the top of the Hit Parade. The song, then published, sold over one million copies and a like number of records. The published version did not acknowledge Bob Fletcher. Porter later stated that this was an "oversight" committed without his knowledge, as he was in the hospital at the time.

A story in the January 22, 1945, issue of Newsweek implied that Fletcher's contribution ("nothing but the title and a couple of words remained at the finish") was minor indeed. This impression has been reiterated by virtually every Porter biographer and almost every article that has appeared about the song. The story was further confused by the rash statements of Fletcher's friends. One of them, a Montana newspaper publisher, printed an editorial accusing Porter of stealing Fletcher's song. Walter Winchell picked up the item, and his version led to people calling Fletcher an "antediluvian cowboy" trying to cash in on Porter's good fortune. Fletcher, of course, had sold the song to Porter outright and had no further claim to it. Nevertheless, Fletcher was quite justified in his disappointment over not receiving credit in the published copies of the song. Porter later made amends for the oversight of his publishers by signing over a portion of the royalties on the song to Fletcher even though he didn't have to.

Still at issue after thirty-five years is the extent of Fletcher's contribution to Porter's lyric. That question can now be answered. Here is Fletcher's original lyric for the refrain of "Don't Fence Me In":

[Fletcher's title not shown]
(Bob Fletcher)

Don't fence me in.
Give me land, lots of land,
Stretching miles across the West,
Don't fence me in.
Let me ride where it's wide,
For somehow I like it best.
I want to see the stars,
I want to feel the breeze,
I want to smell the sage,
And hear the cottonwood trees.
Just turn me loose,
Let me straddle my old saddle
Where the shining mountains rise.
On my cayuse
I'll go siftin': I'll go driftin'
Underneath those Western skies.
I've got to get where
The West commences
I can't stand hobbles
I can't stand fences,
Don't fence me in.

And here is Cole Porters' lyric.

DON'T FENCE ME IN
(Cole Porter and Bob Fletcher)

VERSE 1

Wild Cat Kelly, looking mighty pale,
Was standing by the sheriff's side,
And when that sheriff said,
"I'm sending you to jail,"
Wild Cat raised his head and cried:

REFRAIN

Oh, give me land, lots of land under starry skies above,
Don't fence me in.
Let me ride thru the wide-open country that I love,
Don't fence me in.
Let me be by myself in the evening breeze,
Listen to the murmur of the cottonwood trees,
Send me off forever, but I ask you, please,
Don't fence me in.

Just turn me loose,
Let me straddle my old saddle underneath the Western skies.
On my cayuse,
Let me wander over yonder till I see the mountains rise.

I want to ride to the ridge where the West commences,
Gaze at the moon till I lose my senses,
Can't look at hobbles and I can't stand fences,
Don't fence me in.

VERSE 2

Wild Cat Kelly, back again in town,
Was sitting by his sweetheart's side,
And when his sweetheart said,
"Come on, let's settle down,"
Wild Cat raised his head and cried:

REPEAT REFRAIN

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Note from Joe Offer (30 March 2012): I checked the Kimball book again, and it does indeed say in the first line that the song was published in October 1944. Note, however, that the Kimball book says that Cole Porter sent a copy of "Don't Fence Me In" to Bob Fletcher on January 7, 1935, saying that the song would be published the following autumn. Nonetheless, the Kimball book and the Levy Sheet Music Collection say the song was published in 1944.