Getting your Hrvatski zavod za zdravstveno osiguranje or in other words HZZO is luckily also fairly easy.
HZZO is the Croatian health insurance which you basically need to sign up for if you want to stay (and you want to after going though the permit application nightmare).
Getting the HZZO can be different from office to office and even depending on which country you are from. But here is one way to get it.
Before being able to obtain your HZZO you need to have your Residents permit or be far in the process, and to get this you need your EHIC card. So until you get your permit and HZZO you should still be covered. But the moment you are no longer a resident of your home country – your EHIC will be invalid. (and Croatia do not want you to be uninsured)
During process with the police, they will give you a request letter for you to take to HZZO. This letter proves that you intend to reside in Croatia and the Policija have tentatively approved you for residency.
Once you get this document from the Policija, you’ll need to take it to HZZO. There are no forms to fill out at HZZO, merely an exchange of documents. HZZO will then give you a letter showing that you are now insured that you will take back to the Policija to be added to your visa application. It’s actually a fairly easy process.
After this you will be send a bill, and you are ready to register with a doctor.
After some time you will receive your main card and will continue to pay a monthly fee of 422 kunar a month. You do not get bills each month! It is for you to go to the Post Office each month, fill in a slip, and pay. You can pay as much as you want at a time and save yourself a lot of trips to the post office.
Just to confuse things the bills are paid to the Finance Ministry not HZZO!