If the dog was bought during the marriage, he is considered personal property just like any other. Until a Court rules one way or another, your husband should not remove any personal property from the home unless it is agreed upon. Unfortunately, without the benefit of having filed for divorce, he or you can do whatever you want with marital property. You can seek relief by filing for divorce. Once the divorce is filed the courts normally issue a pretrial standing order that would prevent him from removing personal property, to include the dog. Until then, you both have equal rights to the dog. I would say the only exception may be if you were given the dog by a third party. If that is the case, the dog would be your separate property.