The family of a Brooklyn woman killed when police opened fire on a gunman near a West Indian Day Parade route has filed a notice of intent to sue the city and the NYPD.

The notice claims that cops fired what it calls an “errant” bullet that killed 56-year-old Denise Gay as she sat outside her Crown Heights home on Sept. 5.

It was filed with the Office of the Comptroller, and details plans to seek $10 million in damages.