The Department of Investigation announced Thursday that it will scrutinize management of all city juvenile lock-ups, less than two weeks after three teens ditched a Brooklyn group home and were charged with raping and robbing a 33-year-old woman.

The investigative agency said it arrested Denzel Thompson, 24, the worker responsible for monitoring the teens at Boys Town in Park Slope, for allegedly falsifying records that indicated he’d kept a close watch on them.

The 16-year-old suspects — Eric Pek, Emanuel Burrows and Sanat Asliev – were arrested June 2, a day after they met the woman at a Lower East Side Internet cafe, then allegedly beat and raped her in a park.

The city’s Administration for Children’s Services quickly shut down the group home, which was operated by Boys Town under a $19 million city contract.

Boys Town has three other local facilities — one in Queens and two in Brooklyn. All three remain open.