Ah, Connecticut. I used to live there. The problem with Connecticut schools is that switching districts is next to impossible. Also, there are clear boundaries between the rich neighborhoods and everyone else. This means that the rich neighborhoods continue to get good funding and the rich kids are sent there without having to pay any money. However, if you're in a non-rich district then your education is basically fucked. It's a horrendous cycle over there.
Here in Washington, switching schools is as easy as giving waivers to both districts and (provided you're not a kid with a history of violence or anything) you'll be accepted. When you switch districts, your taxpayer dollars that would normally be sent to the school district you were originally zoned for are sent to your district of choice instead. This creates competition and flexibility among the districts. They will actively try to improve their schools with the money they get, which in turn will attract more taxpayers.