N.M. Stat. § 70-3-6
[Private telegraph or telephone line along right-of-way of
pipeline.]
The owners or operators of any pipelines for which any right-of-way is obtained
under the provisions of this act shall be entitled to erect and construct a telephone or
telegraph line upon and along such right-of-way for use in the operation of such
pipeline, and shall not be required to operate said telegraph or telephone line as a toll
line, or to open same to the use of the public; provided, that the construction and
maintenance of said telephone or telegraph line shall not unduly interfere with the
cultivation of any agricultural land.