@mfroiz , assuming that you are a US citizen/Resident ( Green Card ) whom have worked abroad for the last two years and have returned home , then start of residency for the State tax purposes is generally ruled by the State laws . Often this is the date when you re-established your physical presence in the state.
I am not sure that this is what you meant -- so please explain in what context are you looking for the date when you established residency. There seems to more there in this question
