Family members of citizens of European Economic Area (EEA) or Switzerland, who are nationals of third countries, are entitled to free movement in accordance with Directive 2004/38/EC of 29 April 2004, which the Republic of Croatia transferred into her national legislation.
A family member of a citizen of EEA/Switzerland can travel without a short-term visa to Croatia if he/she has a valid passport and a valid identification card called "Residence card of a family member of a Union citizen", and if he/she travels with or joins the family member who is citizen of EEA/Switzerland.
If a family member of a citizen of EEA/Switzerland does not have such card, he/she needs a Croatian short-term visa.
In cases when family members of the EEA/Swiss citizens travel with or are joining a family member who is an EEA/Swiss citizen, and they require a short-term visa, they are given a priority appointment for submission of short-term visa application directly at the Embassy/Consulate. Such applications are processed in expedited procedure, without charging short-term visa fee, and with minimum documentation: short-term visa application form, valid passport, photo, and proof of family relationship with a citizen of EEA/Switzerland.
For all other travel purposes, i.e. when they are not travelling with or joining a family member who is an EEA/Swiss citizen, short-term visa application procedure is standard, and visa fee is charged.
The text of Directive 2004/38/EC is available here:
http://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:02004L0038-20110616&qid=1460703510422&from=EN