A Broadway actress fought off a would-be rapist in Central Park yesterday by bashing him with her purse, cops said

The woman, 30, was intoxicated as she entered the park at West 64 Street at 2:30 a.m. yesterday, and the man began to help her.

He then tried to rape her, but ran off with her purse after she fought back, cops said.

Police are hunting for the suspect, who was caught on a nearby surveillance camera, walking without a shirt.

The actress was being treated for cuts and bruises at Mount Sinai Hospital.