The girl of his dreams / Donna Leon.

Enhanced descriptions from Syndetics:

Donna Leon's Commissario Guido Brunetti mysteries have won legions of fans for their evocative portraits of Venetian life. In her novels, food, family, art, history, and local politics play as central a role as an unsolved crime. In The Girl of His Dreams when a friend of Brunetti's brother, a priest recently returned from years of missionary work, calls with a request, Brunetti suspects the man's motives. A new, American-style Protestant sect has begun to meet in the city, and it's possible the priest is merely apprehensive of the competition. But the preacher could also be fleecing his growing flock, so Brunetti and Paola, along with Inspector Vianello and his wife, go undercover.

But the investigation has to be put aside when, one cold and rainy morning, a body is found floating in a canal. It is a child, a gypsy girl. Brunetti suspects she fell off a nearby roof while fleeing an apartment she had robbed. He has to inform the distrustful parents, encamped on the mainland, and soon finds himself haunted by the crime--and the girl. Thought-provoking, eye-opening, and profoundly moving, The Girl of His Dreams is classic Donna Leon, a spectacular, heart-wrenching addition to the series.