 Dubai and Ras al Khaimah are the only emirates that do not conform to the federal judicial system of the United Arab Emirates . The emirate 's judicial courts comprise the Court of First Instance , the Court of Appeal , and the Court of Cassation . The Court of First Instance consists of the Civil Court , which hears all civil claims ; the Criminal Court , which hears claims originating from police complaints ; and Sharia Court , which is responsible for matters between Muslims . Non @-@ Muslims do not appear before the Sharia Court . The Court of Cassation is the supreme court of the emirate and hears disputes on matters of law only . 
