Do I have to sterilize my cat even if it stays inside my home?

No, you are not obliged to sterilize your cat if it never goes outside of your home. 
In the case where there is more than one cat on the property, all cats must be sterilized, with the exception of one cat only. For example, if you have three cats who do not go outside, two must be sterilized.

Are there any exemptions for sterilization of dogs or cats?

Yes, your domestic dog or cat need not be sterilized in the following cases: 
  1. If your animal is under 6 months or over 10 years of age;
  2. If a veterinarian prohibits sterilizing the dog or cat for reasons related to the animal's health;
  3. If your dog is registered with the Canadian Kennel Club;
  4. If your cat is registered with the Canadian Cat Association. 

Must animals sold by pet shops in Brossard be sterilized?

Yes, since 2012, the sale of cats and dogs by pet stores is prohibited unless sterilized and identified by microchip.