Here is the definition of a residence from Nebraska Department of Education Rule 19.
"002.14 Residence shall mean that place in which a person is actually domiciled, which is
one’s established home and the place to which one intends to return when absent
therefrom. It is the place where a person is actually living full-time, as opposed to
vacationing or visiting. It should be noted that, pursuant to Section 79-215 R.R.S. and
this Chapter, a child may have a residence for school enrollment purposes that is
separate from the residence of his or her parents or guardian. An example of such a
situation is when a child resides in a different district than his or her parents, under the
legal or actual charge or control of an adult acting in loco parentis, or an adult who has a
power of attorney under §30-2604 R.R.S. (See also the opinion of the United States Court
of Appeals, Eighth Circuit, in the case of Horton v. Marshall Public Schools, 769 F.2d
1323 (1985)). It should also be noted that the Legislature has provided for several
circumstances in which a person may enroll in a school district other than the district in
which that person has a residence (See Section 79-215 R.R.S. in Appendix C). Lawful
citizenship or presence does not determine residency."
Every district is supposed to have an adult with charge or control of a child claiming to be a resident student fill out Appendix A of Rule 19 for enrollment. A parent would have to fill out residency information on the enrollment option application form in those cases as well. If a parent or parents were to submit false information, that could be a Misdemeanor under state law, (abuse of public records, 28-911). That would be a matter for local law enforcement.