Anyone who deals in Latvian property has certain tax and maintenance obligations to perform. First and foremost, one must properly register and pay all the one-time taxes at the time of transaction. For example, property sellers need to pay capital gains tax, and buyer must register with a Land Book. The convenient thing is that you will probably not be able to seal the deal without doing all that, which means that any property agency will make sure everything has been done. After that, it all depends on your ownership status and your aims.
If you are any kind of real estate owner, i.e. you are registered as an owner in appropriate Land Books, it is also your obligation to pay the real estate tax.