Tenn. Code § 35-50-101
It is lawful for any party of whom a bond, undertaking or other obligation is required to agree with the party's surety or sureties for the deposit of any or all moneys and assets for which the party and surety or sureties are or may be held responsible, with a bank, savings bank, safe deposit or trust company, authorized by law to do business as such, or with another depository; provided, that the other depository is approved by the court or a judge of the court, if the deposit is otherwise proper, for the safekeeping of the money or assets and in such manner as to prevent the withdrawal of the money or assets or any part of the money or assets, without the written consent of the surety or sureties, or an order of the court, or a judge of the court, made on such notice to the surety or sureties as the court or judge may direct; and provided further, that the agreement shall not in any manner release from or change the liability of the principal or sureties as established by the terms of the bond.
T.C.A. § 35-50-101