Now that her ne’er-do-well boyfriend is accused of killing a cop, Kim Dykstra is finally talking to the police about him.

Dykstra spent yesterday with detectives probing the slaying of Officer Alain Schaberger, who died in Brooklyn on Sunday when George Villanueva, 42, pushed him off the stoop of a Boerum Hill brownstone, authorities say.

Villanueva had been busted several times on charges of beating Dykstra. But each time, she refused to testify against him, said law-enforcement sources.

So Villanueva went free.