It happened just before 7:00 a.m. Friday in the parking lot of the Meadow View Apartments in the 8100 block of Algon Avenue.
Police say a 29-year-old man shot a 22-year-old woman multiple times before turning the gun on himself.
Both were transported to the hospital where the man was pronounced dead. The woman is in extremely critical condition.
Police had previously said she died.
The shooting remains under investigation.
Police say both people involved knew each other.
Their identities have not been released.