Joseph Smith Papers explains Joseph’s choices for Vice President before Sidney Rigdon, James Arlington Bennet and Solomon Copeland.
Council of Fifty, Minutes, March 1844–January 1846; Volume 1, 10 March 1844–1 March 1845, p. 240, footnote 486, The Joseph Smith Papers
At the state nominating convention held 17 May in Nauvoo, the Latter-day Saints declared their support for Sidney Rigdon as the candidate for U.S. vice president. Rigdon was originally from Pennsylvania. The U.S. Constitution prohibits members of the electoral college from casting votes for both a president and vice president from the same state as the elector. To reduce the chances of the election of a president and vice president from different political parties in a close contest, parties avoided nominating a president and vice president from the same state. JS and his supporters first asked James Arlington Bennet of New York to run as JS’s vice presidential candidate but retracted the offer after coming under the incorrect impression that he was not born in the United States. They next asked Solomon Copeland of Tennessee, a friend of Wilford Woodruff, to run for the office; no response from Copeland has been located.
Go to Footnote 486 to see this explanation.