You can prove to either CT or NY that it's not your primary residence for tax purposes, but even if you can't, you may still be better off paying double taxes to avoid a 15 - 20% pay cut.
The pay cut mentioned for Connecticut is 15% and that likely doesn't cover the RSU, so the realistic cut in the pay rate may be more like 5-10%, depending on your function and level. NYC marginal tax rate for a typical Google employee is going to be around 10%. And that's before you take into account the actual cost of this scheme.
