In the case of a tie who determines the outcome of a presidential election?

The US House of Representatives will then decide the election, as they did in the years 1801 (Thomas Jefferson and Aaron Burr tied) and 1825 (John Quincy Adams was 2nd highest in the electoral voting, but won). In the House, each state's delegation receives a single vote.

Similarly, the Vice President is supposed to be elected by the Senate, choosing from the top two candidates. However, the possibility of having a Vice President of a different party than the President is still remote. The only use of this procedure was in 1837, and Martin Van Buren's Vice Presidential running mate, Richard Johnson, was elected 33-16.