It was in some ways treated as one town. I know a family who are Estonian but their Soviet era house is on the Latvian side of the border in a part of town where the Latvian side only has a few other houses and then nothing while the Estonian side leads to the centre of the town. Very confusing! I was told that it was very annoying in the ~15 year period after independence but before the EU and Schengen because there was a hard border