How the Croatian alphabet
Lesson 4: Church records
Vital records (birth, marriage, death) in what is today Croatia were kept for centuries by the Catholic church -- through various government changes -- up until right after WWII when the Yugoslavian government also started keeping vital records (but the Catholic church still continues with its same records). In some cases these church records have been destroyed, lost or misplaced but for the most part they reside at either the State Archives or at the local churches throughout Croatia. The range of years varies. It is common for church records to go back into the late 1700s. I've seen some that go back into the 1500s (Korc"ula, for example). For a history of Catholic church vital records, especially for the region around Rijeka, see here.
Explanation of Matic"ne Knjige and Stanja Dus"a
Here is an explanation of the 4 types of Croatian vital records available in Croatia. These all originated in the churches but some are now kept by the State Archives.
At the moment, the only Croatian vital records available outside of Croatia are the LDS microfilm series of Matic"ne Knjige. These can be ordered and viewed at any LDS Family History Center. There are over 3500 of these Centers throughout the world and probably one near you. The charge is around $3.50 per roll, it takes around 2 weeks for the Center to get them after you order them, and you must view them there at the Center. Most Centers have a machine that creates photocopies from microfilm. The original documents for this LDS microfilm series (the "state copy" of the matic"ne knjige) are explained in the link directly above.