Before you could ever think about going after a centaur, while also finding out that Hoof Hollow actually exists, you needed help with capturing it, because they sound stronger, and smarter than humans. The answer to your help was right in front of you, as you were facing the sign for the Sheriff's Office.
The sheriff was a reliable part of any western town, because a ton of criminals in these times always cause trouble for anyone who would be wielding a gun. Seeing how there were centaurs being close to the western town all the way from Hoof Hollow, you thought that it wouldn't really be a problem for the sheriff considering who it was. You arrive in front of the sheriff's office, and open the door, while hoping to see what the sheriff was up to when you see him, or her come out of the cell room.