If you have no taxable income then there is nothing you can do on a tax form or the IRS to get money or a deduction for a support animal, or any other medical expense. Tax deductions decrease your taxable income and reduce your tax. If you have no taxable income, there is nothing to deduct FROM.
In turbotax if you were claiming a medical expense deduction, you go to the deductions and credits page and click on Medical Expenses. In some cases, if medical is not displayed, you may need to scroll down and look for something like "show more choices" or "skip and show me everything." Once in the medical expense interview the program will walk you through a series of categories and ask for your expenses (prescriptions, medical devices, doctors fees, and other categories). At the end there is "other." You can also only deduct medical expenses that are more than 10% of your income. (If your income was $50,000 and you had $8000 of medical expenses, your deduction would be $3000.) Turbotax will do the calculation for you.
But you won't accomplish anything unless you have a high enough taxable income to pay tax and a high enough list of itemized deductions to benefit from medical expenses.
If you think there is a state tax benefit for a support animal even when you have no income, you would have to check with your state.
