I found this article: Ring the Bell: Reviving an Old Tradition from the Hinds County [Mississippi] Gazette. They are talking about ringing the bell to announce that court is in session.

By searching for "ring the courthouse bell" (and variations, such as ring + "courthouse bell") with Google, I found several references to ringing the bell on special occasions such as Memorial Day, Independence Day, Christmas Day, the anniversary of 9/11, and also about ringing it as a curfew, or on the hour, or to alert volunteer firemen.

Here's a story about a New Year's Eve tradition.

Here's a story about using the courthouse bell to announce births and deaths. (I believe a similar tradition once existed in England, except it was the village church bell).

Here's a story about a 1912 trial at which the judge "issued instructions that the custom of ringing the courthouse bell be dispensed with."

This page about Chester, OH, says that children "especially like the story about the courthouse bell, how every courthouse had a bell, and why. That was because in the old days, they had no telephones, so the only way that they knew that the court was in session was the bell rang. And then if the person was free, they were innocent, with a bell ring. If he was guilty, the bell tolled."

There's probably more info out there, but I sort of got tired of looking.