Pets, for most people, become members of the family. While not given the same consideration as children, many divorces have seen the couple fighting tooth and nail over Rover. Under the letter of our law, nonetheless, pets are viewed simply as a marital asset and, as an asset, a pet may have great monetary value (such as a pure-bred championship-winning dog) or next to none (such as a feral cat taken in and made a house pet). An ill pet could also be a liability.
If the couple cannot decide who will get the pet(s) (or how they will share it (or them)), the Judge might simply assign a monetary value to the pet(s) and treat it (or them) like a sofa.
Frequently, testimony – in a contested divorce – can reveal to the judge that only one party had any true attachment to the pet and that the other’s interest in it is just a negotiating ploy. That could help the judge decide which party should receive the pet, but the pet’s value would also go into that party’s “column”.
In the end, sharing time, care and expenses of the pet may be the best compromise. Also remember that, with rare exceptions, both parties will outlive a pet by a considerable margin.