Police yesterday offered a $12,000 reward for information on the murder of a beloved Brooklyn grandfather — and remain baffled by the slaying.

Stevenson Blackett was killed Thursday just before 2 a.m. while his family slept upstairs.

Blackett, 60, was shot in the head by two assailants who bound his arms behind his back in the basement of his Canarsie home.

A side screen door was cut, and cops are trying to determine whether the killers used a key or Blackett let them in, sources said.

The home appeared ransacked, and investigators took inventory to see what, if anything, was taken, sources added.