Ahem. I don’t think so.
The country with a system most nearly like the U.S. in that regard is probably Switzerland.
The original founders (inhabitants of villages in what is now known as Uri, Schwyz and Unterwald) formed a “league of mutual assistance” in 1291, which date is traditionally considered to be the “birth” of Switzerland. From 1291 until 1798, the city-states making up Switzerland were a loosely-based federation with each “canton” (or state) having its own government, but with a federal assembly to decide mostly on military affairs involving all the cantons.
But after many turbulent events, including:
[ul][li]revolutionaries inspired by French’s revolution taking control of the country in 1798[/li][li]Napoleon imposing a constitution and forming the Helvetic Republic[/li][li]recognition of neutrality in 1815 at the Congress of Vienna[/li][li]civil war between Catholic and Protestant in 1847 when Catholics decide to form their own separate alliance[/li][li]federal constitution of 1848[/li][li]revised (and current) federal constitution of 1874[/ul][/li]
Switzerland came to its current state. The constitutions of 1848 and 1874 were directly inspired by the U.S. constitution, so we have a congress divide into senate (two per canton) and house of representatives (proportional to population), a federal executive and judiciary, etc…
The federal executive power is a council of 7 persons, elected by the federal assembly (congress.) One of the members of the federal council becomes president for a year in a “round-robin” fashion. Switzerland currently has a woman president, its first.
Swiss citizenship is granted by the individual “communes” (or cities), not by the federal government (but the federal government reserves the right to disapprove the citizenship application.)
Switzerland has a “referendum” system where a private citizen can organize a country-wide vote on any legislative matter as long as the requisite number of signatures are collected.
Workers of the world, unite! You have nothing to lose but your chains.