IN HIS LAST BOOK, Blood Brotherhood, Robert Barnard accomplished two things: he wrote a good mystery and also exposed, gently but surely, the hypocrisies and the human facilities of modern churchmen. This time Barnard turn his attention and wit to the affairs of a struggling provincial opera company in northern England. In Death on the High C's (Walker. $7.95), Superintendent Nichols, who knows that Don Giovanni can be sung by either a baritone or a bass, almost brings down the curtain with the arrest of the killer during a performance of Rigoletto. Once again Barnard proves that a satisfying mystery can have delightful moments of humor.

It is sad that Barnard St. James didn't give as much attention to concocting a credible mystery as he did to recreating Napoleon's Paris in April Thirtieth (Harper & Row, $8.95). The result would have been a superior period mystery. Instead, St. James, like a good-glove, no-bat baseball player, writes a lively scene with no plot punch. Until the letdown of the denouement (which barely worked for Agatha Christie and doesn't here), St. James had been moving along quite smartly with his tricorne-hatted Chief Inspector Blanc, and such minor characters as Tellyrand and the painter David. It is a touchy case for Inspector Blanc, as Madame de Besancourt, found strangled in her salon, had been a courtesan with influential lovers.