I'm not going to try and sway you otherwise, but sometimes the only difference in data or perceptions between (a decent) public school district, and a private school is that public institutions are required to be transparent.

For example, low test scores in a public school are indicative of the fact they are mandated to be inclusive of students with special needs. Behavioral issues may also be present at the same level, but these things are not logged as vigorously and are not FOIable as they are in public schools.

I was once told, while working at a private school, to lie to a parent about their child's progress and to inflate the student's grade to keep the family happy and the student enrolled. Unfortunately, I had to comply since there was no union and I needed the job.

There are definitely good private institutions for sure but the private school I was at was a travesty on many levels, but it didn't appear to be that way from the outside. Just a thought.

Oh and if the school is for profit, don't trust it for a second. Yes. For profit schools are a thing in CT.