Per wikipedia he was found guilty of
Count 1 (waging wars of aggression, and war or wars in violation of international law)
Count 27 (waging unprovoked war against the Republic of China)
Count 29 (waging aggressive war against the United States of America)
Count 31 (waging aggressive war against the British Commonwealth of Nations)
Count 32 (waging aggressive war against the Kingdom of the Netherlands)
Count 33 (waging aggressive war against the French Republic)
Count 54 (ordering, authorizing, and permitting inhumane treatment of Prisoners of War (POWs) and others)
My question is which counts were deserving of an execution? Was a war of aggression or an unprovoked war a capital crime? Or was it for Count 54, inhumane treatment of prisoners and others?
Well, its rather tricky to say, and without records of the judges' specific reasoning any answer I give would by necessity be speculation. In the International Military Tribunal for the Far East, nearly all of the accused who were executed were found guilty of either Count 54 or 55, occasionally both, as well as some measure of Counts 1-39. The exception was Iwane Matsui, who was found guilty of only Count 55. However, Mamoru Shigemitsu was also found guilty of Count 55 ("deliberately and recklessly disregarded their duty" to take adequate steps to prevent atrocities.), and recieved only seven years imprisonment. Kuniako Koiso and Shunroku Hata were also similarly convicted and received sentences of life imprisonment. So, based on the evidence, while it would be fair to assume that Count 54 is therefore the basis of his hanging, considering that all others found guilty of Count 54 were also executed, the execution of Matsui (and the correspondng imprisonments of Shigemitsu, Koiso and Hata) shows that the final sentencing was left more to the judges' discretion than to a pre-set sentencing for specific counts (of which the IMTFE Charter contained none, specifically stating in Section V, Article 16 "The Tribunal shall have the power to impose upon an accused, on conviction, death or such other punishment as shall be determined by it to be just."), and that the exact reason for Tojo's sentencing to death by hanging is unknown except to speculation without a primary source pertaining specifically to the judges' deliberation prior to final sentencing.
My source is the transcript of the IMTFE Charter and Judgment of 4 November 1948.
Not a source, but a useful compilation of the above as a table