If you are looking for vital statistic records, those are kept in Lincoln for all the counties in Nebraska after I believe 1904. Some counties kept some records. I believe I paid $8.00 for death certificates, $8-12 for birth records.
I have gotten marriage records, birth and land docs in Beatrice at the Courthouse. I don't remember what the charge was. I don't know if they will do a search for you, but it can't hurt to ask.