Question is only if they do it automatic, and I think this is not the case because at this time as it would be too complicated. Imagine only 28 EU states and their tax offices, if Bitstamp send all of them users data it would be too much work for them, and also there is a question of protecting such data when they leave exchange. Probably they report any suspicious account, especially if there is any doubt about terrorism.
Since people withdraw fiat to their bank account from Bistamp it is under the authority of bank to report to tax office, or in some cases tax office has a complete insight in bank accounts of clients. In this case there is no reason to Bitstamp report anything.
If you read their Terms Of Use this is what they say :
Disclosures to legal authorities and authorized financial institutions
We may share your Personal Data with law enforcement, data protection authorities, government officials, and other authorities when:
Required by law;
Compelled by subpoena, court order, or other legal procedure;
We believe that disclosure is necessary to prevent damage or financial loss;
Disclosure is necessary to report suspected illegal activity; or
Disclosure is necessary to investigate violations of our Terms of Use or Privacy Policy.
We may also share information concerning US citizens who are Bitstamp customers with other financial institutions, as authorized under Section 314(b) of the US Patriot Act, and with tax authorities, including the US Internal Revenue Service, pursuant to the Foreign Account Tax Compliance Act ("FATCA"), to the extent that this statute may be determined to apply to.
https://www.bitstamp.net/terms-of-use/ltd