Form W4 applies to federal withholdings only. Your ND employer is not required to withhold ID taxes, but can do it voluntarily if he agrees. However, remember that ND can tax you as a non-resident on your earnings from working in ND. Therefore it is actually to your benefit to have ND taxes withheld.
Here is what ID says about your situation:
Idaho residents working in other states
If you're an employer and your employee is an Idaho resident but is working in another state, you generally don't have to withhold Idaho income tax. Instead, you should withhold tax for the state in which the employee is working. You should contact that state to be sure of its withholding tax laws.
If the other state doesn't require withholding, Idaho tax can be withheld if both you and your employee agree.
Form W4 applies to federal withholdings only. Your ND employer is not required to withhold ID taxes, but can do it voluntarily if he agrees. However, remember that ND can tax you as a non-resident on your earnings from working in ND. Therefore it is actually to your benefit to have ND taxes withheld.
Here is what ID says about your situation:
Idaho residents working in other states
If you're an employer and your employee is an Idaho resident but is working in another state, you generally don't have to withhold Idaho income tax. Instead, you should withhold tax for the state in which the employee is working. You should contact that state to be sure of its withholding tax laws.
If the other state doesn't require withholding, Idaho tax can be withheld if both you and your employee agree.