N.M. Stat. § 55-3-414
Obligation of drawer.
(a) This section does not apply to cashier's checks or other drafts drawn on the
drawer.
(b) If an unaccepted draft is dishonored, the drawer is obliged to pay the draft (i)
according to its terms at the time it was issued or, if not issued, at the time it first came
into possession of a holder, or (ii) if the drawer signed an incomplete instrument,
according to its terms when completed, to the extent stated in Sections 55-3-115 and
55-3-407 NMSA 1978. The obligation is owed to a person entitled to enforce the draft or
to an indorser who paid the draft under Section 55-3-415 NMSA 1978.
(c) If a draft is accepted by a bank, the drawer is discharged, regardless of when or
by whom acceptance was obtained.
(d) If a draft is accepted and the acceptor is not a bank, the obligation of the drawer
to pay the draft if the draft is dishonored by the acceptor is the same as the obligation of
an indorser under Section 55-3-415(a) and (c) NMSA 1978.
(e) If a draft states that it is drawn "without recourse" or otherwise disclaims liability
of the drawer to pay the draft, the drawer is not liable under Subsection (b) to pay the
draft if the draft is not a check. A disclaimer of the liability stated in Subsection (b) is not
effective if the draft is a check.
(f) If (i) a check is not presented for payment or given to a depositary bank for
collection within thirty days after its date, (ii) the drawee suspends payments after
expiration of the thirty-day period without paying the check, and (iii) because of the
suspension of payments, the drawer is deprived of funds maintained with the drawee to
cover payment of the check, the drawer to the extent deprived of funds may discharge
its obligation to pay the check by assigning to the person entitled to enforce the check
the rights of the drawer against the drawee with respect to the funds.