Sirius confessed to Dumbledore about being an Animagus when Dumbledore visited him after he was brought to the school by Snape in PoA. Dumbledore tells the trio this. So it wouldn't have mattered when Snape went running to Dumbledore to tell on Sirius.
Originally posted by Squb Kitten
I think he may have told Dumbledore in the aftermath of the PoA incident, but it was quite hectic then, and DD probably would have just brushed him off. Snape wouldn't have told the Ministry, they would not have trusted his word, while they would believe DD. So it would have been up to DD to tell the Ministry, and he did not do that, obviously, for his own reasons.
If you remember, on the train Draco said to Harry,
Originally posted by Squib Kitten
Also, the Death Eaters knew in OotP that Black was an Animagus, because remember how Snape told Sirius that Lucius had seen him on Platform 9 3/4?