'Cops' Shootout Suspect -- Family Compares Omaha to Ferguson ... Police Were Showing Off

Omaha police officers were running and gunning to make compelling TV when they sprayed bullets at an armed robbery suspect, killing him and a 'Cops' crewman ... so claims the dead suspect's family.

TMZ spoke with one of Cortez Washington's relatives ... who believes the officers used excessive force Tuesday night -- and were "hyped up" to put on a good show when they responded to the Wendy's.

As we reported ... 'Cops' sound supervisor Bryce Dion died after getting hit by friendly fire from Omaha PD during the shootout with Washington -- who was holding a Wendy's employee at gun point.

Washington's firearm turned out to be a pellet gun -- modeled after a real semi-automatic pistol -- and his family thinks officers should have recognized it wasn't a lethal weapon before they unloaded more than 20 rounds. One family member told us, "With everything going on in Ferguson, you think they would use other options."

The relative also said they don't buy Omaha PD's claim Cortez started the shootout by firing two rounds.

Omaha cops say they were not grandstanding for cameras ... maintaining they responded to the robbery with proper protocol ... and engaged Cortez because he pointed and fired his weapon at them.