T-Boz Watkins, from TLC, believes cops gunned down her cousin in cold blood at the end of a standoff ... and she's demanding justice for her family.

The shooting happened last Wednesday in Peoria, Illinois -- police responded to a bank robbery and, after using surveillance video to identify the suspect as Eddie Russell Jr. ... tracked him down to a home. Police surrounded the home for 2 hours before 25-year-old Eddie emerged.

While police describe Eddie as aggressively advancing "toward officers with a handgun" -- T-Boz disputes that and says her cousin was unarmed. She also blames cops for "using" Eddie's mother to lure him out of the house. Her biggest issue is he had mental health issues, and she claims police knew that, and promised his mother they would "give him the help he needs."

Cops admit firing 18 shots, and say the coroner confirmed Eddie was struck 17-20 times. They also say they recovered a handgun that matches the one he allegedly had in the bank.

Police released an image from the surveillance video, but T-Boz isn't buying that's a gun in Eddie's hand. Now, she's just trying to get word out about what she considers a senseless killing.

Illinois State Police are investigating.