We do not file electronically so I assume that it takes time for the SAR to be available to law enforcement through the Gateway program-right?
From the last credible explanation I heard, it may be 5 - 7 weeks before a SAR filed on paper is accessible electronically via the Gateway mechanism. (Yet another argument for filing electronically.)
Since you filed the SAR, you have the safe harbor in terms of relevant disclosures to law enforcement. Regardless of what you are
encouraged to do, you should discuss the issue with your bank's legal counsel. Since you used the term "detective," I assume state or local law enforcement is conducting the investigation. Your attorney will be able to say whether there is a state statute that expressly authorizes the disclosure to them. If there is not, it's more of a judgment call.
Acknowledging my prejudices, I have no confidence in the discretion of local law enforcement; I think SAR confidentiality would mean a lot more to me than it does to them. Your attorney's advice should control here, but I would be willing to make the disclosure to the prosecuting attorney assigned to the case. I suggest that your bank's attorney be the one to do the talking if that's the path you take. He or she might ask the prosecutor to subpoena the supporting documentation from the bank. (I understand a subpeona is not required, but if the documents show up as evidence and there was no subpoena any defense attorney capable of finding the court house will back into the fact that a SAR must have been filed.)