This is not covered in the movie.
There is a time jump of over a year between the peace meeting and when we see Michael again.
But it is explained in the novel
....because someone else took the rap. A Bocchicchio clan member.
The Bocchicchio were professional peace-brokers / negotiators and even hostages.
When warring families wanted to make peace and arrange a parley, the Bocchicchio clan was contacted. The head of the clan would handle the initial negotiations and arrange for the necessary hostages. For instance, when Michael had gone to meet Sollozzo, a Bocchicchio had been left with the Corleone Family as surety for Michael’s safety, the service paid for by Sollozzo. If Michael were killed by Sollozzo, then the Bocchicchio male hostage held by the Corleone Family would be killed by the Corleones. In this case the Bocchicchios would take their vengeance on Sollozzo as the cause of their clansman’s death. Since the Bocchicchios were so primitive, they never let anything, any kind of punishment, stand in their way of vengeance. They would give up their own lives and there was no protection against them if they were betrayed. A Bocchicchio hostage was gilt-edged insurance.
The Godfather - Mario Puzo
The Don the instructs Tom Hagen..
"And I want my orders obeyed exactly. But, Tom, the most important thing is we have to get Michael home as soon as possible. Make that first in your mind and in your work. Explore all the legal alleys, I don’t care how much money you have to spend. It has to be foolproof when he comes home. Consult the best lawyers on criminal law. I’ll give you the names of some judges who will give you a private audience."
Eventually, a Bocchicchio already on Death Row was persuaded to confess to the crime.
But it was to be nearly another year before Don Corleone could arrange for his son Michael to be smuggled back into the United States. During that time the whole Family racked their brains for suitable schemes.
Finally it was the Bocchicchio Family who through a misfortune of its own solved the problem.
What happened next had the simplicity of genius. Don Corleone guaranteed to the head of the Bocchicchio clan that the wife and children of Felix Bocchicchio would be rewarded with a handsome pension. The money for this would be handed over to the Bocchicchio clan immediately. In turn, Felix must confess to the murder of Sollozzo and the police captain McCluskey.