Always in Croatia by land and not by ship the passport is not needed once you leave the airport. (other then hotel check in)
John H. states that there is an inspector checking passport so I would take the passport with you.
This could also be something new that they are now doing.
However you may take your passport just to find out that there is no inspector. :|
I would take it if that is what the Cruiseline is telling cruisers to do.
This is what you can say to the inspector.....
Ovoya moi pachaporat....Hvala
(Here is my passport....Thank you)