It would be a joint crash investigation as intuition and history would suggest.
The formal basis for this is generally covered by the Chicago Convention on International Civil Aviation which established the ICAO, The International Civil Aviation Organization in 1944, a specialized agency of the UN charged with coordinating and regulating international air travel.
Cross border incidents are not unknown and the ICAO recognizes LOA (Letters of Agreement) between States that have airports or significant air traffic near common borders. For instance there are bi-lateral agreements between the Netherlands and Germany and Switzerland and Germany as to how Air navigation services and accident investigations are handled.
Similar to LOA, Canada and the United States concluded a bi-lateral agreement in 1963 under the somewhat ponderous title of Exchange of Notes Constituting an Agreement Between The United States of America and Canada Relating To Air Traffic Control.
Essentially recognizing the respective sovereignty of each State's airspace, co-operative operation of air-navigation services and related operational issues.
Lower level government agencies were specifically authorized to set policies for issues not already federally regulated where common interests and agreement were found, with the result that there is a legally sanctioned bilateral agreement to let the accident investigation boards of both countries determine most of the policy for and co-operate in investigating aircraft crashes occurring within 50 miles of the common international border.
The Chicago Convention on International Civil Aviation
Treaties and international agreements registered or filed and recorded
with the Secretariat of the United Nations
Agreement between the Government of Canada and the Government of the United States of America for Promotion of Aviation Safety
Cross-border provision of Air Navigation Services with specific reference to Europe
By Niels Van Antwerpen
(Preceding thesis by the same title)