Need to check if tenant is legal resident in the US ?

[Mary Joe]

Is the landlord responsible for checking if the tenant is a legal resident ?  Say if I am renting to someone who is a student from overseas or who is here on a work visa,  is it the landlord's responsibility to check to make sure that the tenant is staying in the country legally with the proper visa?   

normally I only ask for photo ID such as driver's license.  But one applicant is interested in the property but I believe he said he is here under a work visa or something like that. 

Wonder if anyone has come across situations like this. 

THANKS !!