Final answer:
The mayor-council system is the form of municipal government that mirrors the structure of state and national governments, with separate executive and legislative branches.
Step-by-step explanation:
The form of municipal government that closely matches the structure of state and national government, with a distinct executive and a legislative branch, is the mayor-council system. In the mayor-council system, voters elect both the members of the city council, which performs legislative functions, and the mayor, who carries out the executive functions. This form of government can exhibit varying degrees of authority for the mayor, from a strong-mayor system with significant power to a setup with limited executive powers.