Congratulations on being cast! No, the Constable doesn't sing. He's the "heavy", the bad guy who at first appears to be Tevye's friend, but through the course of the play betrays that friendship. First he tipped Tevye off confidentially to an upcoming "little unofficial demonstration" - which turned out to be the trashing of Tzeitel's wedding reception, then much of the rest of Anatevka. In the movie the Constable (well-played by Louis Zorich) arrived in time to call off the rampage just short of total devastation; in a stage production, he leads it. Either way, Tevye is for once reduced to speechlessness. His final duty is to bring word of the eviction order, then carry it out. Here IMO he proved himself almost totally unprincipled, choosing self-preservation over friendship - and trying to wash his hands of any personal responsibility by claiming to be just following orders. In all fairness, like anyone in the Tsar's service, he had little choice but to follow orders (in the movie he was coldly threatened with replacement). In the end he is ultimately answerable to his conscience for his (in)actions. That principle was well-established at the Nürnberg war-crimes trials of the 1940s, along with the principle that merely following orders blindly is no excuse for atrocities.