Does each county in Nebraska have its own board of elections? I'm sure the big cities do and the town clerks might take care of municipal elections as in Maine, but in Maine federal, state and county offices are all on the same ballot. Thanks for the information rbt48.
Answer: In Nebraska, each county has an election commissioner. The governor appoints the commissioner for a four year term. Also, a deputy commissioner is governor appointed and must be a member of the other major party.
A funny (well, not to him) thing happened in 2006. Many Democrats registered as Republicans just to vote in the Heinemann - Osborne gubernatorial primary. Then, they planned to switch back. The Douglas County (Omaha) Deputy Election Commissioner did this leaving both he and the Commissioner as Republicans. When word of this surfaced, he was fired (they had no choice) and replaced. Poor guy was left unemployed, but perhaps wiser.
Now, to address the thrust of the question, the election commissioner is responsible for any election within that county (county-wide, city, school district, and others). He/she designs the ballots, ensures the votes are counted, handles absentee/early voting, and oversees recounts, mandatory when the margin is >0.5%, I think. The Secretary of State carries these functions out for statewide or multi-county elections, and for state senate races.