Can you deny applicant after verbally approving?

[David B.]

I have a room in basement apartment in my home that I am renting out.  I verbally accepted applicant but we have not signed lease or accepted any monies. The applicant is currently living with a friend.   I have gotten serious cold feet because the applicant has made comments that would indicate they are financially stretched (.. need to  wait for their next pay check to have security and 1st month rent....they would like early access to space so they can take small loads because they don't have enough money to rent a uhaul.) 

Is it too late to back out if we have not signed anything , but I did tell them via text they were approved?