criminal trespass of an entire state

Via NPR this morning. A New Hampshire police chief has charged illegal immigrants with criminal trespass . . . of the entire state. The statute in question is N.H. Rev. Stat. § 635:2 which reads

I. A person is guilty of criminal trespass if, knowing that he is not licensed or privileged to do so, he enters or remains in any place.

II. Criminal trespass is a misdemeanor if:

(a) The trespass takes place in an occupied structure as defined in RSA 635:1, III; or

(b) The person knowingly enters or remains:

(1) In any secured premises;

(2) In any place in defiance of an order to leave or not to enter which was personally communicated to him by the owner or other authorized person; or

(3) In any place in defiance of any court order restraining him from entering such place so long as he has been properly notified of such order.

III. All other criminal trespass is a violation.

IV. As used in this section, "secured premises" means any place which is posted in a manner prescribed by law or in a manner reasonably likely to come to the attention of intruders, or which is fenced or otherwise enclosed in a manner designed to exclude intruders.

The chief's reasoning: they entered the state, which is a place, and they had no license or privilege to do so because they're illegals. Viola: criminal trespass. I am not familiar enough with New Hampshire law to know the difference between a misdemeanor and a violation, but it seems likely that the chief's objective is to get them deported for breaking the law.

Much sound and fury has erupted, but the actual legal battle looks like it'll be more over preemption: because the federal government regulates immigration, has it preempted the state's ability to do what effectively amounts to the same thing?