I’ve been checking into this . You need to go to the Ygeionomiko (ΥΓΕΙΟΝΟΜΙΚΟ - Public Health Dept). In Chania the offices are right opposite the Attikon Indoor cinema entrance on Stefanou Dragouni street (the old hospital street) off Iroon Politecniou street.
There is no sign on this door – it’s the tall grey doors.
They will give you a list of the documents you need (passport copy, a health book from a book shop etc) and the tests you need to do which include a chest X ray, a stool culture and blood tests for hepatits B and C etc.
You need to first obtain the written list from this office in order to get the correct tests done.
If you have IKA (if coming from the UK you may have form E106 etc? Get an IKA health book first – this is for the doctors, not the same as the health book for working in the catering industry but they both have the same name vivliario ygeias / βιβλιάριο υγέιας) you can then go to an IKA GP (pathologos) and he will give you IKA prescriptions for the tests. You’ll then need to book appointments with IKA for each test and take your IKA prescription with you for each test appointment. The tests will then be free.
If you are not covered by IKA you’ll have to get the tests done privately. They’ll cost around 30 to 50 euros for each test.