Not in exactly so many words, but I think he would have if the conversation hadn't gotten sidetracked:
First, Ron sees Sirius, with a knife in Gryffindor tower:
"... I was asleep, and I heard this ripping noise, and I thought it was in my dream, you know? But then there was this draft... I woke up and one side of the hangings on my bed had been pulled down.... I rolled over... and I saw him standing over me... like a skeleton, with loads of filthy hair ... holding this great long knife, must've been twelve inches... and he looked at me, and I looked at him, and then I yelled, and he scampered."Then, in the Shrieking Shack, Black admits to having had Crookshanks steal the passwords:
"This cat isn't mad," said Black hoarsely. He reached out a bony hand and stroked Crookshanks's fluffy head. "He's the most intelligent of his kind I've ever met. He recognized Peter for what he was right away. And when he met me, he knew I was no dog. It was a while before he trusted me.... Finally, I managed to communicate to him what I was after, and he's been helping me. .. "What do you mean?" breathed Hermione.And then later, Dumbledore is talking to Harry & Hermione right before Hermione uses the Time-Turner:
"He tried to bring Peter to me, but couldn't... so he stole the passwords into Gryffindor Tower for me.... As I understand it, he took them from a boy's bedside table...."
"Sirius has not acted like an innocent man. The attack on the Fat Lady -- entering Gryffindor Tower with a knife -- without Pettigrew, alive or dead, we have no chance of overturning Sirius's sentence."