N.M. Stat. § 39-4-10
No execution shall issue against any security on any promissory note, bond, bond for costs, appeal bond or other obligation for the payment of money or property, until execution shall have been first issued against the principal in any such note or obligation, and levied upon all the real estate or other property of said principal, which may be within the jurisdiction of the court, in which the judgment may have been rendered: provided, that whenever the plaintiff in any such execution shall file in the court, in which the judgment is pending, an affidavit in relation to such security or securities similar to the one required by law to be filed previous to issuing an attachment, then in such case execution shall issue simultaneously against the principal and the security against whom the said affidavit be filed.
NMS § 39-4-10