Having worked with someone who used to work in a Force Vetting role at PSD (not ASP though), my knowledge is if it's organised or persistent crime and you live at the same address it's a flat no. If it's a one off and it's not you, and it's declared and explained (without an opinion, i.e. 'She didn't do it but was found guilty') they can assess it. Unfortunately if you failed because of it they cannot tell you why!