Just as it is a mistake to assume that the rules governing the replacement of Tom DeLay on the ballot in Texas were the same rules governing the replacement of Robert Torricelli on the ballot in New Jersey, it is a mistake to equate either of these with the rules for replacing Ohio’s Bob Ney, who has announced he will not seek reelection to the House. Each of these rules are set by the state, not by the federal government, even though these are all races for seats in the U.S. House or Senate.
Ed Still noted some of the applicable rules for replacing a withdrawing a U.S. Senate candidate. Now comes word that Ney’s handpicked replacement, State Senator Joy Padgett, may not be eligible to be appointed in his place. Washington Wire, via Political Wire, reports:

State Sen. Joy Padgett, Ney’s hand-picked successor for his seat, could fall under a little-known provision of Ohio election law, dubbed the “sore loser” provision. It prevents a candidate who loses in one primary from running in another during the same election cycle. Earlier this year, Padgett was the primary running mate of gubernatorial hopeful James Petro, who lost to the ticket of Ken Blackwell and his running mate, Ohio State Rep. Tom Raga.
Even if Padgett succeeds in getting her name on the new primary ballot, the controversy could invite other Republicans to jump into the unexpected race. James Harris, who lost to Ney in the Republican primary in May, said he’s considering running again– although the sore loser provision may apply to him, too.

The relevant provision appears to be Ohio Revised Code section 3513.052(B):

(B) The secretary of state or a board of elections shall not accept for filing a declaration of candidacy and petition, a declaration of intent to be a write-in candidate, or a nominating petition of a person seeking to become a candidate if that person, for the same election, has already filed a declaration of candidacy, a declaration of intent to be a write-in candidate, or a nominating petition, or has become a candidate through party nomination at a primary election or by the filling of a vacancy under section 3513.30 or 3513.31 of the Revised Code for:
(1) Any federal, state, or county office, if the declaration of candidacy, declaration of intent to be a write-in candidate, or nominating petition is for a state or county office…