Tiny Tim is a cat with a broken leg that appears in A Special Sesame Street Christmas. Maria finds the cat in the alley behind 123 Sesame Street -- the injured cat had slipped on an icy fire escape. Maria dresses the cat up with a red ribbon, and puts a cast on its broken leg.
They show the cat to Oscar, who accuses it of breaking into his trash can on November 19th and stealing two fish.
In the end, Oscar has a change of heart and takes the kitten in, declaring "Are you people gonna stand around singing while that poor cat freezes? Hey, hand him up here."