It probably would not matter whether they were natural citizens or not. From a liability standpoint alone, no department would allow a "civilian" to be involved in a case.
Then you have the chain of custody problem. A good defense lawyer would use their presence to taint whatever case was developed against a suspect.
That said, many years ago, when i was in college, I took a criminology class funded by the LEAA. As part of the class, we rode a week's worth of shifts with Atlanta, Georgia PD. We were in cadet uniforms, had had background checks and quite a bit of training. These were regular patrol officers, not detectives.
Understand, I think tours and controlled ride-alongs are possible, but not working near or on an actual case.
But it was almost 40 years ago and the climate is more liability-driven now than it was then. There are people on here with more recent experience, that may be able to give you a more definitive answer, but based on the liability and chain of custody aspects, I would sincerely doubt any department would let that happen. Good luck.