Well, the question that comes to mind is how is your power brought to the building? Does your power company bring power and a ground to your fuse box? Are the transformers that bring your power to your building grounded at the pole or grounded at the building fuse box or both?
I don't know anything about how Latvian power companies bring you power or even if there are rules governing this in Latvia. In the USA we have rules governing power input to buildings and homes, and I know how it is configured. If you have a pole ground only, this could explain why you have 120 volts to ground, but only a few millamps, depending on the type of soil, the moisture content, etc., V=IR, or in this case, I=V/R.
AS far as telling you whether you should connect a ground or not connect a ground, the unforeseen circumstances can create some undesired effects. Without knowing all of the facts it is impossible to give good advice.
Sorry for the lack of a good answer...