I will try to make it as short, yet detailed, as possible.
My nephew had some legal problems and police want to speak with him, arrest/charge him. It's nothing major, couple of counts of theft/fraud under $5000.00

He's been depressed lately, probably because of this issue, as well as because of some family problems (with his girlfriend and mother of his child). Depressed as in talked about suicide, planned it, even disappeared for a few days and told a few of family members he'll do it (sent us pictures of how he plans to do it).

What can we do to help him? I'm worried if he goes to police he'll be detained without them giving him any help for his mental health issues. What if he commits himself for mental health issues, or if he goes to the police, turns himself in and tells them about this?

First a couple counts of under 5000 is not going to be jail time.
Next if the US, each state has its own rules on mental health. But in general minor or even major depression is not going to be enough to effect court.
It may be considered for sentencing.

The best they can do, is turn yourself in and get probation and fines, Then also, at the same time, start getting counseling.

"Helping" a young, irresponsible adult is a double edged sword.
Letting family know he's depressed and suicidal is a good sign of wanting help. Disappearing and sending pictures of suicide plans is pure manipulation, an extension of his entitled life.
Let him know that you are there for him whether he talks to the police or checks in to a hospital, but that he's an adult, and you are not there to make his decisions. Since it sounds like he doesn't have insurance, the hospital isn't going to keep him long, but they will set him up with outpatient counselling.
He should do that first, but whatever he does, hope he realizes he should do it sooner rather than later.