If no Vice Presidential candidate gets a majority of votes in the Electoral College, a Contingent Election will be held in the Senate to elect a new VP.
Normally, if a vote in the Senate is tied, then the VP (as President of the Senate) casts a tie-breaking vote. However, if the incumbent VP is also a candidate in a contingent election, this can be seen as a conflict of interest.
Is there anything in the US Constitution, US Code, Rules of the Senate, or elsewhere, that would require the VP to recuse him/herself from such a vote? Or would (s)he be able to vote regardless?