Custody of the family dog or cat or other pets has long been viewed as property in NY divorce cases to be divided like other marital assets. However, more recently the NY Courts have been following an approach of "best for all concerned". So what does that mean, some Courts have tried to reference the numerous factors that could be considered in making the determination if the separating couple cannot come to an agreement. The divorcing couple will each have the burden of proving that the pet "will have a better chance of living, prospering, loving, being loved in the care of one [party] as opposed to the other."
The relevant factors have included: who can best meet the pet's daily physical and emotional living needs, time constraints of each party and their availability for the pet, type of home and yard if relevant, safety concerns, ability to financially care, access to veterinary care, access to socialize with other pets and any other factors that could influence the Court to determine that the pet's future success will be more readily met with one person or the other. I would also suggest that if there are children in the house, the pet should most likely stay with the primary residential parent.
So, now there are standards for pet custody, which in a different way are not so unlike child custody which uses the catch phrase "best interests of the child".
In the past I have resolved these cases without a judicial determination as the parties either agree to a schedule or they decide between themselves which person will the pet live with.