PITTSBURGH — Pennsylvania State Police were justified in fatally shooting a Massachusetts man who abducted his ex-girlfriend’s 8-month-old daughter and held a knife to her throat after leading police on a car chase, a prosecutor announced.

Allegheny County District Attorney Stephen Zappala Jr. said police “did a heck of a job” in cornering the suspect, Jared Brown-Garnham, 21, of Taunton, Mass., and saving the baby from harm after a chase that ended early Dec. 7.

Dash cam video from a police car that chased Brown-Garnham showed him taunting police, pulling the baby from a rear seat onto his lap — during which he motioned with a 5-inch buck knife that he would harm the baby — and stabbing himself in the leg several times.

Police issued an amber alert after the suspect, who had been living in Uniontown, took his ex-girlfriend’s car from a store lot in Brentwood — with the child in a rear car seat.

The woman was giving the suspect a ride to the bus station in Pittsburgh, where he was supposed to board a bus to Massachusetts. Instead, police said, the pair argued, and Brown-Garnham took the car after they stopped at the store.

The baby suffered superficial knife wounds to her neck but was otherwise unharmed.