Adolf Hitler was officially and legally declared dead with the verdict (AZ II 48/52) of the District Court of Berchtesgaden from October 25, 1956 (legally effective from December 3,1956):

VERDICT

It is determined that Adolf Hitler, born 20. April 1889 in Braunau am Inn is dead. The time of death is determined as 30. April 1945, 15:30, following the 80-page expert witness testimony delivered on August 1, 1956. [...] The examination of 42 witnesses, conducted between 11. November [1955] until 15. October 1956, especially such persons that had been still present in the Reich chancellery on 30. April 1045, as well as the evaluation of all documents as well as the national and international testimonies has, to the exclusion of any doubt, revealed that Adolf Hitler ended on 30. April 1945, 15:30, in the bunker of the Reich chancellery in Berlin via suicide, to wit via a gunshot into the right temple. The death of Adolf Hitler is thus to declare in application of § 45 [et c. ...].

There's really not much more to it. Hitlers death by suicide was a known fact shortly after May '45, and this was just the final legal act confirming his fate (it's still Germany, so he had to be declared officially dead by a state authority, not the least to solve troubles and questions about his estate). The question of Hitlers possible survival has been discussed on this sub already a few times, suffice it to say that no one seriously considered the possibility of Hitler surviving. Which didn't hinder conspiracy theories and myths surrounding his death popping up and staying powerful up until the modern day.

As /u/Astrogator correctly pointed out, no one believed that Hitler was still alive in this period and there were no real contingency plans in existence for such a possibility. However, if in some hypothetical situation Hitler was in hiding and caught, he would have been subject to the same international war crimes tribunal system and not West German law. The London 4-Power Agreement was technically still in effect and the UN's International Law Commission had codified a number of the IMT's positions on war crimes and how their violation was a matter for international law. Hitler, in his capacity of head of the German state, would have been subject to these international legal principles since German war crimes occurred in multiple jurisdictions. Although both the ILC and the 4-Power Agreement was pretty dormant in the postwar period after 1949, they still were available legal tools. For example, the Soviets invoked the 4-Power Agreement in response to the ascent of the former Wehrmacht general Adolf Heusinger to the Inspector General of the Bundeswehr and Chairman of the NATO Military Committee. In 1961, the Soviet ambassador to the UN demanded that the US government arrest Heusinger for war crimes on the basis of the Four-Power Agreement. Both the American and FRG press portrayed this demand for a trial as an attempt to split the Western alliance and the US State Department called it "a crude and ludicrous propaganda exercise." While Heusinger's case was less about justice and more political theater, it does demonstrate that the ability to invoke international tribunals were not completely absent in this postwar period. Although the international component of the tribunal system had atrophied after the IMT, this legal principle remained on the books and it is not an unreasonable postulation that it would have been the only real way to try a Hitler that somehow had survived the Battle of Berlin.