Derrick Foster is charged with assault and trespassing in this incident.
He's accused of attacking women in the past.
In this case, police said Foster started following the woman closely after she got out of her car at the garage. He allegedly kept gaining on her, so she ran out onto Gayoso, where other people were around.
Police say Foster took off, but was apprehended by garage security when he came back minutes later.
The head of garage security says the woman was on her way to the Peabody, where she works as a housekeeper.
He also says Foster is banned from the garage for allegedly harrasing other women in the past.
Foster has a lengthy criminal history. He recently pleaded guilty to assaulting a woman at another downtown location and is banned from that property too.