They cannot establish a crime against the prostitute without your statement and testimony in court. They cannot do that here without the prostitute's, or some other actual witness', testimony. The evidence code requires that the state prove up that a crime occurred before any statements of the Accused admitting to the crime can be admitted. You don't have to testify against yourself. However, the cops cannot establish the 'corpus delicti', the evidence that a crime occurred, without your statement. In this case, you made a statement to the cops admitting to a crime. They do not have probable cause, even with your statement.
