We have situations were a customer disputes a debit card transaction for fraud. We investigate and find out that it is a relative or friend of the customer, they do not want to press charges. We refund the customer the money under Reg E and we the bank want to press charges. We are being told by a police detective that we as a bank cannot press charges- only the customer can. Does anyone else run into this? Or are other Banks able to press charges since they victim of the loss?
Any help is appreciated.

I believe if the bank customer is not willing to press charges then you deny the claim as an authorized transaction.

And then you get in line for the CMPs being issued by the regulators for this very reason.

I have had mixed results with these conversations. But even the detectives who understand that the bank, as the financial-loss-holding-victim, can press charges, they still really want the customer involved, because it is the customer who can testify that a transaction is unauthorized.

Randy is exactly right (of course) that you can't deny a claim because a customer is not willing to press charges. The FDIC's new Consumer Compliance Supervisory Highlights briefly explains this:

Discouraging the filing of error resolution requests. .... the FDIC has observed financial institutions implementing onerous requirements for initiating an error investigation or resolving consumer error claims. Some of these have included.... .... (3) requiring consumers to file a police report; and/or (4) requiring consumers to agree to assist law enforcement and/or serve as witnesses in any action brought against the individuals responsible for the unauthorized transaction.

The full publication can be found here: https://www.fdic.gov/regulations/examinations/consumercomplsupervisoryhighlights.pdf

So do other banks press charges or are they just eating the loss and taking the debit card away from the customer?

Ask anyone involved in cleaning up after the mess the Bureau found at USAA FSB (see https://www.bankersonline.com/topstory/160325) about handling customers' Reg E error claims.

Just to clarify- We are accepting the dispute and reimbursing the customer- I guess what I mean with the pressing charges would be to try to recoup the money we wrote off.

Yes, you are now the aggrieved party (unless it can be proven that the claim was a fraud), and, although LE might be less sanguine about pursuing the matter on the bank's behalf, you certainly can pursue the matter civilly if you have a suspect.

As the financial victim you are allowed to seek restitution from the perpetrator. However, depending on the law enforcement agency, they may express little interest in coming to the "deep pocketed" bank's aid. I work with many clients in Chicago who find that law enforcement is more focused on violent crime than a family member or friend who steals a debit card.

The reaction you are seeing from other posters is in response to reasonwhy's suggestion that you use the victim's refusal to work with law enforcement as justification to deny the claim.