(a) Parks acquired under this chapter are under the control and management of the municipality or county acquiring the park. The commissioners court or the governing body of the municipality may by agreement with the Parks and Wildlife Department turn the land over to the department to be operated as a public park. The expenses of the improvement and operation of the park shall be paid by the municipality or county according to the agreement with the department.
(b) A historic or prehistoric site, historical museum, or historically significant object acquired under this chapter is under the control and management of the municipality or county that acquired it.