The European Union is a party to the United Nations Convention on the Rights of Persons with Disabilities. A broad scope of the UNCRPD provisions makes it covered by different types of EU competence – exclusive and shared. In result, the EU and its Member States may exercise their competence in Convention issues to a different extent – depending on the matter concerned. Considering that it becomes clear that a particular mechanism of cooperation between them is required. It should serve a proper implementation of the Convention. This contribution aims at presenting the basic rules governing the cooperation between the Council, the Commission and the Member States in relation to UNCRPD’s implementation as settled by the relevant Code of Conduct. The analysis starts with the status of the EU as a party to the Convention and the division of competence between EU and Member States in Convention-related matters. Then, the rules for establishment and presentation of EU and Member States positions regarding the Convention issues are described. Next, the problem of focal points and nominations to Convention organs as a part of the implementation process is referred to. The last part concerns briefly the evaluation of the institutional aspects of UNCRPD’s implementation which was done by Convention bodies. 