Honestly, I wouldn't look at accreditation. There are four Montessori schools in our small city. Only one of them is accredited. It is an AMI school. We chose to enroll our son in that one.
We are now ending what has been a two year nightmarish experience by pulling him out of Montessori entirely and going with a Reggio Emilia school. Leaving Montessori was not our first choice, but because of the nightmare from the first school, there was no other M-school willing to take a chance on him, even though he was successful in another M-school's summer program. the first school told such outrageous stories of his behavior that the second school was scared to enroll him for the year.

My gut told me not to go with the first school two years ago, but the fact that they were accredited, and had a beautiful campus, and some wonderful features made me ignore my instincts. Never again.
While I know that Montessori claims to "follow the child" we found that this was a false promise at our AMI school, and that their only solution to issues was to follow the child straight to a therapist's office. When the three specialists we went to said there was nothing wrong, they told us we went to the wrong specialists, and should have used the specific people they prefer.

I am sure there are good AMI schools, but we found that the one we chose clung so tightly to their dogma that they preferred to find something wrong with the children than to do any critical self-reflection on how they might need to modify the environment to make more children successful. they had close to 30-40% of the children seeing therapists (OTs and psychologists mainly) because they were unable to self-regulate enough to be successful. When we suggested that maybe their expectations were developmentally inappropriate, they accused us of being helicopter parents.
Anyway, long story short: don't use accreditation as your deciding criteria. Ask thoughtful and critical questions of the people at the school, and choose a school that can give you solid answers as to how they solve problems. Telling you, "there really aren't behavior issues here because the normalization process prevents it" is NOT a good answer.