I dont recall much of that movie except that it was a psychological thriller, and a verse was scribbled on a dilapidated wall. In one scene, the villain impersonates a nurse and escapes from the lunatic asylum or some place where he was confined. I dont recall much else so am sorry for the vague details.
I think the phrase that you're looking for is "My daddy is a dollar / I wrote it on a fence / My daddy is a dollar / not worth a hundred cents."
I am pretty sure this is the movie because this is what the killer keeps on writing on the asylum. The movie is In Dreams and I think its very much similiar to the type of the movie you mentioned about. It has the same scene where killer when he was a kid escapes the asylum in the disguise of a nurse who works there.
Here is the youtube trailer. Hoping this is the one you are seeking.