Tex. Code of Criminal Procedure § 2A.004

(a) A commissioned peace officer of a state adjoining this state, while the officer is in this state, has the same powers, duties, and immunities as a peace officer of this state who is acting in the discharge of an official duty, but:

(1) only:

(A) during a time in which the officer has physical custody of an inmate or criminal defendant and is:

(i) transporting the inmate or defendant from a county in the adjoining state that is on the border between the two states to a hospital or other medical facility in a county in this state that is on the border between the two states; or

(ii) returning the inmate or defendant from the hospital or facility described by Subparagraph (i) to the county in the adjoining state from which the inmate or defendant was transported under that subparagraph; and

(B) to the extent necessary to:

(i) maintain physical custody of an inmate or criminal defendant while transporting the inmate or defendant; or

(ii) regain physical custody of an inmate or criminal defendant if the inmate or defendant escapes while being transported; or

(2) only while the officer is:

(A) in a municipality some part of the municipal limits of which are within one mile of the boundary between this state and the adjoining state; and

(B) regularly assigned to duty in a county, parish, or municipality that adjoins this state.

(b) A peace officer described by Subsection (a)(2) may also enforce the ordinances of a municipality in this state described by that subdivision if the governing body of the municipality authorizes that enforcement by majority vote at an open meeting.