Page "Vice President of the United States" Paragraph 51

The separate ballots for President and Vice President became something of a moot issue later in the 19th century when it became the norm for popular elections to determine a state's Electoral College delegation.

Electors chosen this way are pledged to vote for a particular presidential and vice presidential candidate ( offered by the same political party ).

So, while the Constitution says that the President and Vice President are chosen separately, in practice they are chosen together.