If we knew that it was members of the burgeoning "Magic Task Force" we saw in the latest Kumiko Quest entry who were going to be the first responders we'd talk to here, then I'd actually be willing to take a chance on them, but we don't know that. If it ends up being regular cops who start questioning us in the rubble of this, our most collateral damage-heavy conflict to date, then it's kind of the worst introduction to the authorities we can have up to this point. Technically they'd be obligated to arrest us for vigilantism, even though I don't think they'll actually try it unless we fail our rolls really badly.
One of the reasons for going with Alice's Full Support earlier this turn, was so that we could have people who actually know what they're doing help us get in positive contact with the more important authority figures (like Superintendent Sakurada). But she hasn't had time to actually set the company up yet.