IMEE -
depends on your home state for residence, your tax home, the state of income source, and the duration of the work,...
they can all have differing definitions,...
the safe bet is to continue your state witholding as it is and then let your CPA and TA make the adjustments on your quarterly or annual return, whichever applies,...
let your CPA and TA have as much prior notice as you can for tax filing so they are not assessing your liability under any filing deadline crunch,...
if you do approach crunch time, file for an automatic extension and then let them work it over the late spring and summer,...
it's rarely the tax due that knocks people for a loop, it's the fees, penalties and "others",...