Texas Local Government Code - LOC GOV'T § 323.008. Participation With A Municipality

(a) If a county library is established, the governing body of a municipality that maintains a free public library may notify the commissioners court that the municipality desires to become a part of the county library system. After the notice is given, the municipality is considered to be a part of the system, and the residents of the municipality are entitled to the benefits of the library. Property in the municipality shall be included in determining the amount to be set aside in the county free library fund for county library purposes.

(b) The commissioners court of a county that has established a county library may contract with the governing body of a municipality that maintains a free public library to extend county library privileges to the municipality's residents to the extent and for consideration as the parties may agree. The consideration paid by the municipality shall be deposited in the county free library fund. On the making of the contract, the library privileges are extended to the residents of the municipality.

(c) After a municipality has been a part of the county library system for two years, the governing body of the municipality may withdraw from the system by giving notice of its intention to do so to the commissioners court. The notice must be given at least six months before the withdrawal. On withdrawal, the municipality is no longer entitled to participate in the benefits of the system, and the property located in the municipality may not be included in computing the amount to be set aside for county library purposes. Before the governing body may give the notice of withdrawal to the commissioners court or before the governing body may retract the notice of withdrawal after it has been given to the commissioners court, the governing body must publish another notice once a week for six consecutive weeks in a county newspaper circulated throughout the municipality and designated by the governing body. The published notice must state the nature of the proposed action and the date and location of the meeting at which the proposed action is to be taken.