Nope

This is why I was asking how to detect them yesterday - both Du Shama Gold Universal PLC and LTT 15461 Company had mainly criminal missions. They are the only 2 I think are criminal factions - I think Union of Du Shama Confederacy went up because it it in a war with LTT 15461 Company. If I go back tomorrow I'll snapshot their missions.
We may be using slightly different definitions of criminal missions here, then. It's not just illegal ones, it's a specific set of illegal missions that only Criminal factions offer.
Checking my current station the best way to tell seems to be the assassinations - most factions go for Terrorist or Pirate, the criminal faction goes for Politician. Similar themes on the massacre missions. This system doesn't have any smuggling missions, but again those would usually be for the criminal faction only.
Other detection methods:
- opens black markets at their bases (but this could also be Social ethos, or nowadays in Civil Unrest)
- provides the bad guys for normal courier/trade missions
- wars with everyone (but you need a lot of data to be sure)
- is
targeted by everyone else's pirate/terrorist massacre/assassination missions