In Peycheck v. Rutherford, the Court of Appeals said:

[I]t is well settled that non-custodial parents may be given credit against their child support obligation for payments made on behalf of their children if such payments are for necessaries that the custodial parent either failed to provide or refused to provide. However, the credit for necessaries cannot exceed the amount of support due for the period during which the necessaries were furnished. The obligation to provide necessaries requires the provision of appropriate food, shelter, tuition, medical care, legal services, and funeral expenses as are needed. What items are appropriate and needed depends on the parent’s ability to provide and this issue is to be determined by the trier of fact. . . .
In order to maintain a successful claim for necessaries, the plaintiff must prove: (1) that the child needed the particular goods or services that were provided, (2) that the defendant had a legal obligation to provide the goods or services, (3) that the defendant failed to provide the goods or services, and (4) the actual cost of these goods or services.

This holding was recently affirmed in the case of State ex rel. DeBusk v. DeBusk in which Father was awarded a credit toward his child support obligation for mortgage payments, insurance premiums, property taxes and maintenance expenses after proving the expenses were necessary for the children and Mother failed or refused to pay them.
State ex rel. DeBusk v. DeBusk (Tenn. Ct. App. Feb. 16, 2010).