When deciding about trusting the police, it is useful to consider the business model they are working under. Many departments are de facto revenue collectors. An interaction with a cop working for such an agency will likely result in you paying them money. Assuming you wish to keep your funds for your own purposes, then any contact with these cops is adversarial, and they are not to be trusted.
Another model for policing is aggressive 'roided up cops who want to bust heads. Their mission objective is to hurt you. They are also not to be trusted.
Some departments, and individual cops, have a mission objective to abate thugs and thieves. While they can generally be trusted in theory, as long as you are not a miscreant, if they are not certain you are not up to no good, the relationship is likely to be adversarial and they will not trust you. There is no reason to trust them if they do not trust you.
One cop asked me for my social security number, which tipped me off that he was corrupt as there would be no legitimate reason for him to have it. I told him I would consider giving him that number if I could reasonably expect to receive income from his agency, and asked him if that were the case. He said that was unlikely and I mentioned that he and I would likely be in violation of the Privacy Act of 1974 if I gave him the number without an expectation of income and without he giving me a Privacy Act Notice as required by the law. He declined to press the matter any further.
I mention this because it made me realize that an encounter with the police would likely cost me money, freedom, health or life, but would unlikely be profitable for me, so it is almost always an adversarial situation and therefore there is no inherent reason to trust them. Let them earn any trust you give them.
