Most recipes I see for tzatziki often call for dill and/or mint. However none of them ever state which kind of mint is needed, it's always just listed as mint. So which mint is best for tzatziki? Spearmint or peppermint? Obviously there are many other less common types of mints which may also work but spearmint and peppermint are the only two common mints (at least from where I am from, maybe it's different elsewhere. Maybe there's only one common type in USA, where most of the recipes seem to come from so perhaps that's why there's no distinction?). 
It refers to spearmint in this case. You can find both spearmint (Mentha spicata, known in Greek as δυόσμος) and peppermint (Mentha × piperita, generally known as μέντα, though that may be used for almost any type of mint) pretty readily throughout most of Greece, but spearmint is much more common in traditional Greek cuisine (peppermint is generally too strong for how they typically use mint), and all the original Greek recipes I’ve seen for tzatziki that call for mint call for spearmint. You can, however, substitute most other mildly flavored mints and get a similar flavor. I’ve used both Mentha arvensis (commonly known as field mint or wild mint) and Menth suaveolens (commonly known as apple mint) before in my own home made tzatziki and the difference was not readily noticeable. 