A lot of people weighing in on forums and elsewhere are saying "yes," and pointing to anecdotal evidence that the Cinemark chain has a policy against concealed carry.
What we haven't determined yet--and with all the gun owners in that part of CO, it should be easy to confirm with a photo (after the crime scene is cleared): Was that particular theater posted?
And here's the thing--even if it was, there's the matter of state law.
Per HandgunLaw:
“No
Firearm” signs in Colorado have no force of law unless they are posted
on property that is specifically mentioned in State Law as being off
limits to those with a Permit/License to Carry. If you are in a place
not specifically mentioned in the law that is posted and they ask you to
leave, you must leave. If you refuse to leave then you are breaking the
law and can be charged.
Per USA Carry:
Places off-limits when carrying:
1. Any place prohibited by federal law (e.g. federal offices or courthouse)
2. Any property of public school grades kindergarten through 12, unless
the firearm remains inside a container in a locked vehicle
3. Any public building that prohibits ALL weapons which posts guards and
permanent metal detectors at all entrances and requires all entrants to
surrender handguns to security personnel before entry