Thank you all for the thoughtful replies — I really appreciate your interest and attention.
As requested, here are the chorus and the two stanzas I remember. These are from hearing the song, probably in the late 1940s or in the 1950s. All that's missing are the first few words of the first line of the first stanza.
Stanza 1:
… of a one way street just beyond the limits of the flatfoot’s beat in the whoopee section of a one horse town stood the tin-roofed tavern of Paducah Brown
Refrain: Paducah Brown, shot for selling liquor (or “likka”) shot for selling likka like he’d always done Paducah Brown, shot for selling liquor shot for selling likka in a one horse town
Stanza 2: The gang started coming in at half past eight Paducah met the dry cop at the tavern gate He handed him a fifty like he’d always done so he wouldn’t come a-busting in and spoil the fun