The FBI, U.S. Attorney and Washington D.C. PD have opened a homicide investigation into the death of former Reagan Press Secretary James Brady who died this week ... 33 years after he was shot.

It's a weird turn ... John Hinckley Jr. shot Brady and Reagan outside a hotel in 1981, paralyzing the Press Secretary and seriously wounding the President.

Hinckley was found not guilty by reason of insanity, and the legal experts we spoke with say it is NOT a case of double jeopardy. Hinckley was charged with assault with intent to kill when he was tried. Murder is a separate crime. 

Nonetheless ... a D.C. police spokesman confirms with TMZ the 3 agencies are conducting an investigation.