The state or an agency of the state may contract with one or more entities to finance, construct, operate, maintain, or manage a criminal justice facility provided, in the exercise of the governmental power, for the benefit of the state in accordance with this chapter and:
(1) Subchapter A, Chapter 494, Government Code;
(2) Subchapter D, Chapter 361, Local Government Code; or
(3) the Certificate of Obligation Act of 1971 (Subchapter C, Chapter 271, Local Government Code).