Potential tenant may have submitted fake employment letter

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I have a potential tenant applied for my room for rent. She disclosed to me that she has bad credit due to her past (unknown, didn't tell me more about it), only been at her current job for 6 months, and submitted 2 e-mail references from current supervisor and previous supervisor. The e-mails do not look legitimate to me. One of the supervisor's e-mail is actually a yahoo e-mail and the other e-mail doesn't have an official supervisor signature and company name at the bottom of the e-mail. 

She has expressed it a few times that she's really interested in my room, however, my gut is telling me to not go with this one because of these circumstances. Should I move on to another candidate?