Are there any circumstances under which there could be an autocratic central government and democratically elected municipal government in a same country n the same time?
Please exclude answers that rely on future technologies (AI, robots, omnipresent sensors). I would like to get an idea could it happen now, or even better if it already happened somewhere.
This has happened in the past, and was prevalent in the late Middle Ages of Europe and the early Renaissance, when centralized autocracies were the theoretical mode of rule, but had limited ability to enforce their will on walled cities.
The Hanse, the walled cities of the United Provinces and the "Republican" Italian city states provide examples of this evolution. A strange example is London, England, where the monarch held court within a city that had its own charter, method of selecting municipal officers and even essentially its own army. Monarchs in England ignored the wishes of Londoners at their considerable peril.
The primary issue here is the cities had a large enough population to man the defences, walls and natural protection (the Dutch in the United Provinces could and did breach the dikes and flood the polders surrounding the cities in order to frustrate the Hapsburg armies sent to quell the rebellion), and were wealthy enough to be worth defending. The citizens also needed the ability to withstand prolonged sieges if necessary, and you will note that most of the examples are either port cities in their own rights, or near enough to a coast or river to transport food and supplies, and make the besieger's lot a miserable one.
In the modern age, examples like Hong Kong and Singapore come to mind, and these city states have many of the features their forebears in the Hanse or the United Provinces did. It is theoretically possible that in some future where the EU breaks up or nations are riven between nationalists and unassimilated immigrants, port cities like Rotterdam or Gdansk might revert to this status as well (North American cities like San Diego, Galveston or Montreal might undergo the same political evolution if circumstances change drastically, and you can write your own backstory for other cites in the world).
So, yes, cities can quite easily remain democratic even if they are embedded in a more autocratic nation state.
This exists under pretty special circumstances, namely, it was a British colony for 100 years before reverting to China in 1997. In as much as the British are into democracy and the Chinese (mainland types) are not, there was some negotiation in the 1980s about how re-integration of Hong Kong into China would go. Basically, as terms of peaceful transfer, the British ensured that Hong Kong would keep its market economy, Common law as Hong Kong Basic Law, an an elected chief executive and legislative council.
Unfortunately, this is coming under fire recently, and there are signs of the central government in Beijing moving to crack down on Hong Kong's freedoms, but for at least the last 20 years, the city operated as a autonomous democracy within a autocratic, heavily centralized nation.
This isn't that uncommon today. Consider two major totalitarian governments in the world today.
China has democratically elected, non-partisan local governments not just in Hong Kong (where the government is more analogous to the territorial government of the Virgin Islands or the Puerto Rican government in the U.S.), but also in almost all of its rural villages (at least within core provinces as China as opposed to ethnically distinct ones).
Saudi Arabia likewise has elected local governments in most of its municipalities. Indeed, it even allows women to vote and run for office in these elections. The elections are not entirely free and fair, but it isn't a fully authoritarian non-democratic form of local government either.
The trick is to limit the authority of local governments so that they can't pose a significant obstacle to central government initiatives.
An interesting situation happened within the Holy Roman Empire with Free imperial cities like Ravensburg, Aachen, Frankfurt and Hamburg. The government type in these cities ranged from patrician based oligarchies to democratically elected officials. The free imperial cities were under authority of the emperor rather than a local lord or bishop.
Italian city states of the time could also be included, as they were considered part of the HRE as well, such as Venice, Milan, Mantua, Pisa, Genoa.
edit: Milan might not count as it only had a very small period of democratic rule during the Golden Ambrosian Republic, which was swiftly betrayed and supplanted by Francesco Sforza, who brought autocracy back to the city.
They aren't incompatible. Though you may have to loose your definition of democratic quite a bit.
Universal suffrage may not be a thing. Candidates may not be in a party that opposes the regime, or have to be members of the One Party... If political parties are allowed at all. Voting may not be secret (and rumors of bad things happening to people voting too outside of the line are abundant).
But the people (for a particular definition of 'the people') choosing their mayors among a number of candidates (from a restricted pool of candidates) and their decision being effective? Sure, why not, pretty sure it happens/happened in the real world.
I was going to give the example of the contemporary People's Republic of China as somewhere where this exists, but looks like I was beaten to it! Obviously in the Chinese example there are various formal and informal barriers to democratic participation, but there are also often similar barriers in liberal democracies, so ultimately, your mileage will vary in what you want to consider a democracy or not.
Another option for what you're suggesting could be where representative democracy takes place at one level, but levels above that are run by delegates of those lower level democracies. A rough real-world example of this is the European Union, where national governments are elected by national electorates, but the "European government" (i.e. the Council of Ministers) is made up of delegates from each of the member states. If your setting is some sort of loose federation of city states, where individual citizens primary loyalty is to their city, and each city is wary of relinquishing power and legitimacy to the centre, then this sort of delegated structure would seem very plausible.
This situation occurs under Constitutional Monarchies.
Iran, before the Islamic Revolution, held local elections, but the hereditary Pahlavi dynasty ruled the country.
