DIRECTIVE 2004/38/EC
Family members of citizens of the 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 the European Parliament and of the Council of 29 April 2004 on the right of citizens of the Union and their family members to move and reside freely within the territory of the Member States amending Regulation (EEC) No 1612/68 and repealing Directives 64/221/EEC, 68/360/EEC, 72/194/EEC, 73/148/EEC, 75/34/EEC, 75/35/EEC, 90/364/EEC, 90/365/EEC and 93/96/EEC (Text with EEA relevance) which the Republic of Croatia transferred into its national legislation.
The text of Directive 2004/38/EC is available at: https://eur-lex.europa.eu/eli/dir/2004/38/oj/eng
Family members of citizens of the EEA/Switzerland who have exercised their right to free movement (meaning that an EEA/Switzerland citizen resides in a Member State other than his or her country of origin or travels to another Member State) receive certain procedural facilitations.
RIGHT TO TRAVEL WITHOUT A SHORT-TERM VISA
A family member of a citizen of the 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 a citizen of the EEA/Switzerland.
If a family member of a citizen of the EEA/Switzerland does not have such card, he/she requires a short-term visa (C).
APPLYING FOR A VISA
If 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 (C), 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 (C) fee, and with minimum documentation: short-term visa (C) application form, valid passport, photo, and proof of family relationship with a citizen of EEA/Switzerland.
Ina all other cases, i.e. when they are not travelling with or joining a family member who is an EEA/Swiss citizen, short-term visa (C) application procedure is standard, and visa fee is charged.