They wear bulletproof vests and arrest violent perps. Now city park police are fighting to bear arms.

A week after a madman stabbed five people in Riverside Park in broad daylight, injuring four adults and a 2-year-old boy, Parks Enforcement Patrol officers are demanding the city authorize handguns for them.

“We can get shot, but we can’t shoot back,” said Marlena Giga, who was a PEP officer for 14 years. “We’re police officers without the salary, the title and the gun.”

PEP officers carry batons, cuffs and pepper spray, but the Parks Department says they mainly address quality-of-life violations.

“The NYPD is the city’s primary crime-fighting agency,” a Parks spokesman said.