To claim medical expenses you pay, the person must be your dependent, or be someone who meets most of the eligibility tests but is excluded by their taxable income. In the case of a parent (you are filing jointly with your spouse I assume), they don't have to live with you. The only test that counts is that you must pay more than half their total living expenses. Living expenses include the nursing home, of course, but also might include food, clothing, travel, entertainment, and any other medical expenses. You can claim them as a dependent if you pay more than half their living expenses and their separate taxable income is less than $4300. (Medicaid and social security are not taxable income.). Even if you don't claim her as a dependent, you can claim medical expenses that you pay as long as you pay more than half her living expenses.
Next, is the nursing home actually a deductible medical expense? Yes, if it is a nursing home, and the reason she is there is primarily for medical needs. However, if this is an adult care facility, memory care facility, or assisted living facility (one step down from a true nursing home) then the question is more complicated. I suspect it is a true nursing home, because Medicaid rarely pays the cost of assisted living. However, if this is not really a nursing home and you were using the term loosely, write back for more details.
