Yes. Tax evasion is not legal anywhere, not even in places that have zero tax. So there is a possibility that any bank anywhere can ask to see a tax return.
I couldn't find a definition anywhere of EU member state tiers and what country is in what tier (nor could I find out how many tiers there are), but I can't think of a single︀ EU country where I haven't come across this request. Except maybe in the Nordic countries︁ where the banks can just get tax returns by asking the local tax authority. Perhaps︂ I just haven't experienced Tier 1 EU. But I have seen these requests from banks︃ in Spain, France, Germany, Netherlands, and Switzerland.
Generally speaking, though, the bigger the bank and/or︄ the bigger the economy of that country is, the less likely it is you'll be︅ asked. Smaller banks and smaller countries have more at stake with each individual client so︆ they are more likely to ask invasive questions.