The local police force -- presumably from nearby Brattleboro, Vt. -- play small but significant roles in the beginning and at the end of Sucker Punch. The local police are not to be confused with the Vermont State Police, who appear elsewhere in the movie.
After Babydoll's retalliation against him, her stepfather first calls them saying she just attacked him in an unprovoked manner after killing her sister and went with them to the cemetary where her mom was buried earlier that day. It's possible he may have bribed at least one of them to prevent an investigation or that he may have had at least one friend on the force but before she could fight back, she was sedated and driven to the Lennox House.
At the end of the movie the police are dispacted to the hospital after Vera discovers that her signature was forged on the authorization form to have Babydoll lobotomized. They arrested Blue and his two primary henchmen but with a minor difference between them: Blue was blabbering to them everything about her stepfather whereas CJ and Danforth turned themselves over without a fuss due to either knowing they were busted or they grew a conscence over what they've been doing. Before they leave, the lead officer askes Babydoll if she's okay but doesn't answer due to the lobotomy she sustained a short while ago.