first are you applying for a permit to buy/own a gun or to carry concealed?
different permits and different applications and different permitting authorities.
all your answers will be provided in the statutes that require the permit. is it a state or local statute? then look up the statute online, it will list the questions AND what are valid reasons for denial.... also you need to know if your permitting authority is a MUST issue or a MAY issue.
must issue is just that, IF you meet all the criteria, they MUST issue the permit. in a MAY issue area, the permitting authority has the final determination, they can refuse to issue even you pass all the requirements.