If you have an issue with a wild animal, don't call the police, call animal control. Note that if you have a racoon or possum or other animal that can be caught, it must be killed or let loose. Animal control will not relocate a wild animal. You should also note that it is illegal for you to relocate an animal. You may need to call a professional trapper to deal with the problem.
If you have an issue with a neighbor's pet in your yard, do not contact the HOA or HOA officers, try to work it out with your neighbor. You can use this website to find out who's pet might be out in the neighborhood. Try posting in the forum. If that fails, call animal control.