Probably. If the animal is associated with a health issue then it would be a medical deduction and subject to the 7.5% limitation of gross income before being able to deduct the animals costs. But the dogs costs would be lumped together with the other medical costs for the year as well for your or your family's health care costs.
If is a non-health service animal, it would depend on what the service it is associated with.

You may deduct, as a medical expense on Schedule A, the costs of food, grooming and veterinary care incurred to maintain the animal's health and vitality so that it may perform its duties for a guide dog or other animal if used by a visually impaired, hearing-impaired or other physically disabled person.