Can cops keep my car impounded and everything inside?

I let my friend use my car to get to hospital but on the way there he was pulled over, he took off from cops on foot. The car is mine and I called to see what was going on, and they told me they towed it and had to do inventory on it. I called the police department back later that evening and I was told that they impounded my car until the person who ran turned themselves in. I then asked if I could get my house keys and mail key off my chain and they told me no that my keys were impounded too and continued to tell me that it looks like I’m going to be with car or house keys. Can they legally do this?