I live in a bad neighborhood and have a German shepherd, can I pretend he's a police dog?

I live in a neighborhood on the outskirts of an area that is very high in crime. I take my German Shepherd running with me every night and someone asks me almost every time if he is a police dog. The people that are asking are always very standoff-ish and concerned, almost suspicious looking, and make me a little nervous. To feel a little safer, is it okay to lie and just say " Yeah he is"? Like is it even legal? Or would it even make a difference since I'm already running with a big "scary" looking dog?