New state/bought a house

My husband and I bought a house in NC in February and began moving into in May.  We previously lived in Florida, so did not have state taxes.  His employer will withhold the NC tax, but mine will not.  How do we determine:

  • Do we need to make changes to our Federal Withholding?  (We owed quite a bit last year.)
  • Should we "double up" on state withhold on my husband's taxes?  If so, how do we calculate how much to withhold?

    Thanks!