Alfred Hitchcock was reportedly furious when Brian De Palma decided to make Obsession (1976), because he thought it was a virtual remake of Vertigo (1958). Ironically, De Palma stopped making mystery/adventure films after Hitchcock's death in 1980, with the possible exception of Body Double (1984).
The church seen at the beginning of the film, Church of San Miniato, is different from the one that Michael actually goes into when he sees Sandra. The reason for this is because the priests of the Church of San Miniato would not allow De Palma and his crew to film inside of the church, because of a previous film crew that turned out to be making a porno film, and had told them otherwise. This can be seen clearly when Michael goes into the church, which only has one door to enter into, and then in the next shot, where Michael's back is towards the door, and there are now two, and a windows on the doors that don't match the one that we saw on the outside shot. The collegiate church in the town of San Gimignano was used for the interior shots.
The church in Florence significant in the plot of the film is the Church of San Miniato, or San Miniato al Monte (Saint Minias on the Mountain), a Romanesque basilica built in 1018, on the site of a 4th century chapel.