Should police checks be mandatory for Councillors?

I read a short article on this the other day. It recommended that all elected members would have to have a police check before they could start work as an elected member. I pondered on if this were necessary or warranted. It would be fair to say I probably wouldn't want to have to work with a mass murderer or allow fiscal responsibility to someone found guilty of fraud. Nevertheless, surely if this was warranted it should be available before being able to nominate? In my work these checks are done before we reregister every 3 years, so if I'm still employed I must have met the threshold. That being said we've managed quite nicely without and rarely get to see small children or handle the money directly.