Police have launched an investigation after a woman filmed herself performing a sex act on a man inside a courthouse and posted the video on Twitter.

After sharing the explicit clip online the 26-year-old woman boasted that it was to get her out of trouble without revealing what kind of trouble she was in.

The 34-second video showed a sex act on a bench in a corridor outside a courtroom, but has been deleted from the woman's Twitter account.

The shocking incident occurred during business hours at the Duval County Courthouse in Jacksonville, Florida, and the mobile phone footage was posted online on Tuesday, News4Jax reported.

The woman wrote on Twitter: “Had so much fun at court today. Found a way to get my charges dropped.... Ssssssh don't tell.”

A police report said the sex act was captured by CCTV and consisted of a man and woman engaging in what appeared to be inappropriate behaviour on the fourth floor of the courthouse.

The woman was at the courthouse for a 9am arraignment on charges of possession of drug paraphernalia, smuggling contraband into jail and violation of probation.

Court records show she pleaded no contest, News4Jax reported.

Police have identified the man in the video, the report added.