Can my child's father file against me for leaving the state?

You are probably OK. First, look at the terms of the written permission to relocate from NM. Is it limited to TX, or general as in permission to leave the state? Was there an amendatory court order relating to custody and location? If not, and the father has continuously lived in NM, then any further custodial litigation would be there since that State maintains "Exclusive Modification Jurisdiction." For an explanation, see the article titled "The Basics of Family Law Jurisdiction," on the Published Works page of our firm web site, at http://www.willicklawgroup.com/published_works. If the father ever moved out of NM, then NM lost jurisdiction, and the further litigation would be in the child's Home State -- here, from the facts you provided. See the same article, an the accompanying flowcharts, for an explanation. The oral consent to relocate coiuld be given effect. See: .................... "Moving out of State Without a Court Order not Determinative of Custody, Especially where Verbal Consent to Move was Given" Gepford v. Gepford, 116 Nev. 1033, 13 P.3d 47 (2000) Appeal from order of the district court (Sullivan) granting mother’s motion to modify the decree of divorce to change custody of the minor children. After the parties’ divorce, the (custodial) father parent moved from Nevada to Idaho with the (non-custodial) mother’s oral consent. The mother discovered that one of the children, a 9 year old, had been left alone while the father assisted a friend on a construction project 6 blocks away. The mother called the local police who went to investigate. The police found the situation to be proper as the child was not upset, had food, blankets, and the house was warm. The child also had the father’s beeper number. The mother subsequently filed a motion for a change in custody claiming that the father had moved from Nevada without a court order in violation of the relocation statute, NRS 125C.200, the father had left the child alone and that the father had denied the mother visitation. The Court reviewed the Nevada standard for modifying custody. The standard requires that once custody has been established a court can consider changing the custody only if (1) the circumstances of the parents have been materially altered, and (2) the child’s welfare would be substantially enhanced by the change. Murphy v. Murphy, 84 Nev. 710, 447 P.2d 664 (1968). The Court concluded that the district court abused its discretion in determining that the second prong of the test had been satisfied, since under McMonigle v. McMonigle, 110 Nev. 1407, 887 P.2d 742 (1994), the enhancement to child welfare must be substantial. Again the Court stated that while custody determinations will not be disturbed unless there has been an abuse of discretion, the appellate court must also be satisfied that the district court’s determination was made for appropriate reasons. The Court determined that substantial evidence did not support the district court’s conclusion that the children’s welfare would be substantially enhanced by a change in custody, since leaving a child home alone on one occasion, when the child suffered no harm was, as in Sims v. Sims, 109 Nev. 1146, 865 P.2d 328 (1993), if not an “ideal” choice, “it hardly smacks of a reason to lose custody.” .................... You should probably seek consultation with an appropriate family law specialist. I would suggest starting your search with the American Academy of Matrimonial Lawyers, the Nevada chapter of which can be viewed at http://www.aaml.org/go/fellows/fellows-by-state/?showResults=true&state=NV. Good luck.