A burglar slipped undetected inside the private Manhattan home of the city’s Health Commissioner occupied by her daughter and a friend — and made off with cash and a computer, The Post has learned.

The unidentified crook opened an unlocked sliding glass to enter the house of Commissioner Mary T Bassett on Park Terrace West near Columbia University Football Stadium in Inwood yesterday morning, sources said.

While her daughter, Aurora Bassett, and a male friend were hanging out, the suspect quietly rummaged through the house without alerting them to his presence, the sources said.

He stole two wallets containing about $300 and a computer, the sources said.

Video surveillance captured the burglar as he left the scene with the stolen merchandise, sources said.