I highly doubt there are many (if any) places with "installing any kind of AC is illegal" laws.
On the other hand, there are plenty of noise-related laws preventing you from installing an AC loud enough to be a nuisance for your neighbors. But that's solved by getting one with proper sound isolation, or placing it in such a way that the noise doesn't travel to the neighboring properties.
Similarly, you aren't allowed to install an AC on the facade of a protected historical building. But that can be solved by installing it on the rear of the building (where it is invisible), or by placing the unit itself indoors and using hidden air vents.
There's also the issue of landlords and HoAs banning you from making modifications, but that's not really a matter of legality.
The rules in NL at least are 45dB during hte day, 40dB at night, at property line.
Our machine in "silent" mode is around 42dB ~60cm from the unit, and we can get it to 40dB with a little distnace from property line and a sound barrier between it and the neighbour. It really is _shockingly_ quiet compared to the dull roar of AC that was ubiquitous to me growing up in central California. (40 dB is "faint" or "computer/babbling brook according to https://soundproofingguide.com/decibels-level-comparison-cha... ) Neighbours still whine about it though. I think they dislike A/C on principle, though.
But making a hole in the wall to the outside is. That would generally be considered a permanent change and requires approval from landlord and in case the apartment building has multiple owners, approval from those as well
On the other hand, there are plenty of noise-related laws preventing you from installing an AC loud enough to be a nuisance for your neighbors. But that's solved by getting one with proper sound isolation, or placing it in such a way that the noise doesn't travel to the neighboring properties.
Similarly, you aren't allowed to install an AC on the facade of a protected historical building. But that can be solved by installing it on the rear of the building (where it is invisible), or by placing the unit itself indoors and using hidden air vents.
There's also the issue of landlords and HoAs banning you from making modifications, but that's not really a matter of legality.