I am not certain, because I would have to check what the requirements are for Senator.
Maybe someone else can chime in on this?
I do know that the State of Illinois doesn't require a Senator candidate to prove their citizenship. But, past that, I have bad memory or ignorance to plead.
From Article I, Section 3 of the US Constitution:
“No person shall be a Senator who shall not have attained to the Age of thirty Years, and been nine Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State for which he shall be chosen.”
Hussein did lie on his candidate application. That is proveable.