Can I be charged with theft and subpoenaed to take a polygraph if no evidence is found against me?

I was recently working for a moving company when a client said her wedding band was missing. I was already gone from the job site when police arrived and when asked to come back I refused to outstanding traffic warrants and a criminal mischief warrant. I never had the ring and was never seen taking anything. What are my rights as far as refusing to take polygraph or talk to law enforcement? Again I was never in possession of the ring nor have I touched it. What kind of case can they make on pure speculation?