It depends on how suspicious. Like are they walking sideways? or are they talking to themselves? If they were doing something like those two things, I could safely assume that you could cause a disturbance to the peace. I would give them an ultimatum. I'll wait 10 minutes, then if you wont give your name, I'll take you down to the station. I would give no threats or use harsh language. If they give me their name, I would look their records up. If they had similar cases, I would take them anyway. Just incase. It's better safe than sorry.
