Did Michael touch anything else? In the car or in the restaurant. Sollozzo smelled a rat when Michael got up to go to the bathroom. Why? Perhaps because Michael didn't touch the glass, which is a difference to the novel. In the novel he says: "The wine went right to my bladder." (Sorry for mentioning the novel here.)
Anyway, the police would be able to find Michael's fingerprints in the restaurant and probably in the car. Also, if he forgot his hat, they would find his hair.