The establishment of a branch office by a non-EU/EEA credit institution is subject to a reciprocity condition.
"Article 83
(1) A credit institution of another Member State may establish a branch in the Republic of Croatia and provide mutually recognised services that it is authorised to provide in the home Member State through that branch under the conditions laid down in this Act. 
[...]
Article 89
(1) A third-country credit institution (founder) may provide banking and/or financial services within the territory of the Republic of Croatia only through a branch, provided it is authorised to provide such services in the third country.
(2) A third-country credit institution (founder) intending to establish a branch within the territory of the Republic of Croatia shall obtain authorisation from the Croatian National Bank (hereinafter referred to as 'authorisation to establish a branch of a third-country credit
institution'). 
[...]
Article 90 [...]
(4) The Croatian National Bank shall refuse an application to establish a branch of a third-country credit institution if:  [...]
6) credit institutions with head offices in the Republic of Croatia are not provided at least the same conditions for establishment of a branch in the country where the third-country credit institution (founder) has its head office as are provided to the third-country credit institution (founder) in the Republic of Croatia.[...]" (Credit Institutions Act (NN 159/2013; 20 December 2013), as last amended by Law NN 70/2019 of 17 July 2019, Articles 83, 89 and 90 [unofficial translation])
Credit Institutions Act (NN 159/2013; 20 December 2013), as last amended by Law NN 70/2019 of 17 July 2019, Articles 83, 89 and 90
[<a href="https://narodne-novine.nn.hr/clanci/sluzbeni/2013_12_159_3328.html">Act</a>],[<a href="https://www.hnb.hr/documents/20182/506024/e-zakon-o-kreditnim-institucijama_npt.pdf/2ddb8f5f-eec8-b8b4-090f-d92304af0116">Act_Eng</a>]