Authorisation to register a fishing vessel and to fly the Austrian flag is conditional on majority ownership by Austrian or EEA citizens, and is conditional on the majority of the members of a legal person (e.g. managing director, board of directors and the chairman) meeting the requirements of Austrian or EEA citizenship.
"§ 2. 
For the purposes of this federal law,
1. “Austrian seagoing ship”: a seagoing ship that is approved for maritime navigation in accordance with this Federal Act;
2. "Seagoing ship": a vehicle which, depending on its size, type and equipment, can be used for journeys at sea (passenger ship, cargo ship, yacht, special vehicle). A rowing and paddle boat and a type of boat that can usually only be used for trips in the immediate vicinity of the coast are not considered such [...]
6. "Special vehicle": a vehicle that does not fall under Z 3 to 5, in particular [...]
c) Tugboat, fishing vessel, launch,
[...]
§ 3.
(1) The flag of the Republic of Austria at sea (sea flag) in the form in accordance with Paragraph 2 may only be carried by Austrian seagoing vessels; they are not allowed to fly the sea flag of another state.
[...]
§ 7. [...]
(2) Admission to sea navigationg is associated with the right and obligation to use the sea flag.
(3) The Federal Ministry for Transport, Innovation and Technology has to issue a certificate for admission to maritime shipping, which bears the designation Seebrief. This certificate counts as a decision.
[...]
§ 8. 
(1) Admission to sea navigation may only be granted
1. a natural person if they
a) has Austrian citizenship,
(Note: lit. b and c repealed by Federal Law Gazette I No. 46/2012 )
d) is more than 50% owner of the ocean-going vessel,
(Note: lit. e repealed by Federal Law Gazette I No. 46/2012 )
2. a partnership under commercial law, if more than 50% of its personally liable partners who are authorized to represent the company meet the requirements according to item 1 letters a to c, the majority of these persons meet the requirements of item 1 letter e and the company is based in Austria or in the territory of another contracting party to the Agreement on the European Economic Area and has met the prerequisite according to item 1 lit.d;
3. a legal person, if the majority of the members of each of its organs (e.g. managing director, board of directors) including the chairman meet the requirements according to item 1 lit. . a to c, more than 50 per cent of Austrian citizens, the federal government, a state, a municipality or a community association are entitled to the voting rights and the legal person is based in Austria or in the territory of another contracting party to the Agreement on the European Economic Area has as well as fulfilled the requirement according to item 1 letter d;
4. the federal government, the federal states, the municipalities and the municipal associations, if they meet the requirement according to item 1 lit.d.
[...]
(8) Citizens of a contracting party to the Agreement on the European Economic Area are on an equal footing with Austrian citizens. [...]" (Maritime Shipping Act (BGBl. Nr. 174/1981), last amended by BGBl. I Nr. 82/2018, §§ 2, 3, 7 and 8 [google translation])
Maritime Shipping Act (BGBl. Nr. 174/1981), last amended by BGBl. I Nr. 82/2018, §§ 3, 7 and 8
[<a href="https://www.ris.bka.gv.at/GeltendeFassung.wxe?Abfrage=Bundesnormen&Gesetzesnummer=10011537">Act</a>]