Probably not. A nursing home receiving Medicare or Medicaid cannot require a responsible party to co-sign the admission contract. This practice is forbidden by federal law. The law is called the Nursing Home Reform Act (NHR). The NHR states clearly that a nursing home cannot require a third party to guarantee payment as a condition of admission to the nursing home. This law applies to all nursing homes that receive Medicare or Medicaid. If the nursing home does not receive Medicare or Medicaid, it may require a co-signature.
For more information, see: 42 U.S.C. §§ 1395i-3(c)(5)(A)(ii), 1396r(c)(5)(A)(ii) (2015); Joan M. Krauskopf et al., Elderlaw: Advocacy for the Aging §§ 12.10, 11 (2nd ed. 1993).