U.S. Const. amdt. XII —
The Senate president is required by the Constitution to “open all the certificates”.
3 U.S.C. § 15 —
The Act further describes as “all the certificates and papers purporting to be certificates”.
Siegel, Stephen A. (2004). “The Conscientious Congressman’s Guide to the Electoral Count Act of 1887”. Florida Law Review. Vol. 56. p. 541. —
Regarding whether the Senate president can be required to present or not present any particular paper submitted as a states electoral college vote, concurrent action by both houses would settle the matter while disagreement between the houses would see the Senate president’s decision upheld.
(The Senate president is the Vice President of the United States.)
Regarding my earlier reference to the joke, I got the year wrong. In one case from 1889, papers sent as a “practical joke” have been presented to the joint session. (Siegel, Stephen A. (2004). “The Conscientious Congressman’s Guide to the Electoral Count Act of 1887”. Florida Law Review. Vol. 56. p. 541.)