Convicted killer cop Peter Liang and the city have been slapped with a $200,000 lawsuit by the girlfriend of slain Akai Gurley over his 2014 shooting.

Melissa Butler, who tried in vain to save Gurley after he was shot by Liang, says the city was negligent in hiring the rookie cop and his partner Shaun Landau, the suit filed Wednesday in Brooklyn ­Supreme Court charges.

Butler tearfully testified at ­Liang’s manslaughter trial that the two cops didn’t perform CPR as Gurley bled in the darkened stairwell of a Brooklyn housing project the officers were patrolling.

She and Gurley took the stairs that night because the elevators weren’t working.

Liang was convicted on Feb. 11 of manslaughter. He faces up to 15 years in prison.

Butler, who is described as Gurley’s “companion” in the court ­papers, also names the city Housing Authority in the suit.

Butler’s lawyer, Roger Wareham, said she still “suffers a lot from the loss of someone close to her … from just the lack of care or consideration that Liang and his partner showed for Akai.”