Fund in Greenwich - hearing 1BR apartment pays for itself with tax break?

Joining a fund in Greenwich this summer and have heard that by buying a small 1 bedroom or studio in CT and claiming it as primary residence (while still keeping NYC apt) it basically pays for the CT apartment with the tax break. This would remove city tax along with the difference between ny state and CT state tax is.

Has anyone looked into this? Or would anyone know how to run the numbers and look into this a little further? Would appreciate any guidance. Thanks all

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