Do I need to file a non-resident State return if I had earned wages in that state for part of the tax year? (The W-2 does show some withholding for that state.)

Do I need to file a non-resident State return if I had earned wages in that state for part of the tax year?  (The W-2 does show some withholding for that state.)  I have already reported the other state's income and withholding as part of my total wages from all sources in my home/resident State return. Or should I have left the non-resident State income out of my home State's return?