Trying to figure out the name of this old movie?

It is black and white. A comedy/mystery. An older man is strangled and his car driven off into the water. Two detectives from the Yard are sent to investigate because they get a letter from the man who died. On the way to the mansion the blow up a gas station. When they get to the mansion they question the staff, there is a busty maid, a man with his tounge cut out, a butler, and a few others. They also question his daughter. Then they are shown to their chambers where they find secret passage ways and pictures with the eyes cut out. One by one the staff starts to die the disapper, but there are riddles and clues near them. In the end, the man isn't dead at all and his daughter is to blame.