I suspect this could be Rise of the Dragon. It was released in 1990 for PCs (and several other platforms), and is a point-and-click adventure game with a first-person view and pre-rendered, static backgrounds. The protagonist is a private detective who used to be a police officer. The game starts as a murder investigation. It is set in Los Angeles in the ...
I know it's a bit late but I was after a very similar game and just came across it again.
Mission Omega - C64 and Amstrad?
I'd recommend you check it out but you build robots from parts and send them out to explore. Choosing everything from their mode of movement to their weapons and sensors.