Neb. Rev. Stat. § 32-720: Neb. Rev. Stat. § 32-720

(1) In case of a division of any political party, the Secretary of State shall give the preference of party name to the convention held at the time and place designated in the call of the regularly constituted political party authorities, and if the other faction presents no other party name, the Secretary of State shall select a name or title and place the same on the ballot before the list of candidates of such faction. The action of the preceding national convention of such party, regularly called, shall determine the action of the Secretary of State or the court in its decision. The Secretary of State may be compelled by peremptory order of mandamus to perform such duty.

(2) A political party may dissolve by filing a notice of dissolution with the Secretary of State. The notice shall be filed by the executive committee or state central committee of the political party or, if no such committee exists, by an officer of the political party. If the notice is filed prior to December 1 of the calendar year before the statewide primary election, the Secretary of State shall not accept any filings for the political party or place the political party on the statewide primary election ballot for the statewide primary election.