Level 20
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Deductions & credits

A service animal is an animal that has been trained to perform one or more assistive tasks to assist a person with an illness or disability. If your animal is trained to assist you with a disability then you can deduct the cost as medical expenses. 

Support animals -- that provide support through their own natural behaviors but which are not specifically trained to provide assistance -- are more complicated.

"The costs of buying, training, and maintaining a service animal to assist an individual with mental disabilities may qualify as medical care if the taxpayer can establish that the taxpayer is using the service animal primarily for medical care to alleviate a mental defect or illness and that the taxpayer would not have paid the expenses but for the disease or illness."

"A taxpayer who claims that an expense of a peculiarly personal nature is primarily for medical care must establish that fact. The courts have looked toward objective factors to determine whether an otherwise personal expense is for medical care: the taxpayer’s motive or purpose for making the expenditure, whether a physician has diagnosed a medical condition and recommended the item as treatment or mitigation, linkage between the treatment and the illness, treatment effectiveness, and proximity in time to the onset or recurrence of a disease"  "A personal expense is not deductible as medical care if the taxpayer would have paid the expense even in the absence of a medical condition."

https://www.irs.gov/pub/irs-wd/10-0129.pdf

So if you are audited, you would bear the burden of proof for all these factors.  That you did not own the animal before, only bought the animal because you were advised to by your doctor to treat a mental defect or illness, and would not have bought the animal if you did not have an illness.

You would list the expenses along with other medical expenses on the Deductions and Credits page.  To get any benefit, you must itemize your deductions (not use the standard deduction) and your medical expenses must be more than 7.5% of your income.