Is the party nomination something a candidate even can accept or refuse? Or is the nomination more like a glorified endorsement?
Are there obligations that come with accepting the nomination?
At least in some states, Political Party Convention Certificate of Nomination document does NOT require the candidate's signature. E.g. Iowa.
I haven't found a conclusive proof yet, but circumstantial evidence points to the fact that nomination is "binding" in that, if the party persists in its folly and insists that the nominee is the nominee despite their refusal/lack of acceptance, then they will be the nominee, against their will.
The evidence comes from infamous Sherman quote
I will not accept if nominated and will not serve if elected.
Note that this statement was repeated repeatedly including by other figures; with no noticeable criticism to the effect of "Well, if you don't accept; you won't be a nominee so you won't be in a position of being elected".
However, in other states, that's not the case; and active and direct acceptance by nominee is required for ballot access. E.g.
in NY State (based on Gentner v. Albany County Bd. of Elections, 309 A.D.2d 962 (N.Y. App. Div. 3d Dep’t 2003)". Quoting:
Because petitioner was an enrolled member of the Conservative Party, she was required to file a certificate accepting the nomination, signed and acknowledged by her, by July 14, 2003 or the nomination would be null and void.
In Connecticut (Statute CHAPTER 153 - NOMINATIONS AND POLITICAL PARTIES)
Sec. 9-388. Report to Secretary of the State. Whenever a convention of a political party is held for the endorsement of candidates for nomination to state or district office, each candidate endorsed at such convention shall file with the Secretary of the State a certificate, signed by him, stating that he was endorsed by such convention, his name as he authorizes it to appear on the ballot, his full residence address and the title and district, if applicable, of the office for which he was endorsed. Such certificate shall be attested by either (1) the chairman or presiding officer, or (2) the secretary of such convention and shall be received by the Secretary of the State not later than four o’clock p.m. on the fourteenth day after the close of such convention.
And some states it's not entirely clear. E.g.
(1) Partisan candidates for the offices of President and Vice President of the United States on the general election ballot shall be certified to the Governor and Secretary of State by the national nominating convention as provided by law. (Nebraska Revised Statute 32-620)
Theoretically, the party has full control if needed without depending on state rules requiring acceptance.
Having said that: Parties are private organizations and their nominating process is only governed by privately determined convention/nomination rules.
As such, a party - even if that's not in effect currently - can very easily adopt a rule that states that a candidate cannot be a nominee unless they explicitly and formally accept; even if the state doesn't require that like Ohio.