Public Trust DHS

Does having multiple arrests automatically disqualify you from receiving approval?
I was arrested in 2014 for trespassing and disorderly conduct (misdemeanors). The disorderly conduct charge was dropped but i was convicted of trespassing. In 2016 I was arrested for simple assault (misdemeanor) by being falsely pointed out of a group of people at a club. This was later dropped by the person that pressed charges once she learned I was the wrong person.

Would these things disqualify me?