No, assuming the reception facility did not (and most do  not) guaranty that it would keep your belongings safe, you could only sue them for compensation if you can show that they were unreasonably careless. An open cloakroom is common, and would not by itself by unreasonably careless; therefore, they almost certainly would not be liable. Since your coat was likely stolen or taken mistakenly by a third party, the facility would not be liable or responsible for it. You can file a police report, but unless there is some evidence of which person stole it, there is nothing they can do but take the report.