Cinemark has No Guns Policy
John Lott likewise has confirmed this.
Private business owners who invite the public onto their own premises can set their own policies: “Nothing in this part 2 [establishing the scope and limits of a Colorado concealed carry permit] shall be construed to limit, restrict, or prohibit in any manner the existing rights of a private property owner, private tenant, private employer, or private business entity.” Colo. Rev. Stat. Ann. § 18-12-214(5). Source.