If you are a Nebraska resident, you can register with the election office in your home county even if that is in a different county than the one you attend college. Leaving for temporary purposes, such as college attendance, need not result in a change of residence for voting purposes.
You can register in the county you are attending college if that is the place in which you intend to establish a home and be habitually present.
Declaring your residency in Nebraska for voting purposes does not change your residency for tuition purposes.