A few facts:
A Withdrawal Card has nothing to do with withdrawing (resigning) from the Union. You get a Withdrawal Card from your Local (cost: 50 cents) when you will be out of work for a period of time, such as on a layoff of a month or more. This stops your obligation to pay dues while you have no paychecks coming in. When you go back to work, you turn in you Card and resume paying dues.
Anyone, no matter what state they are in, can resign from the Union at any time simply by sending a written note to the Local Secretary-Treasurer saying that you wish to resign. It's best to send it certified mail, return receipt requested.
If you are in a Right-To-Work State, your resignation letter will also stop your obligation to pay dues. In a Non-Right-To-Work State you do not have to pay dues, as such, but you do have to pay an Agency Fee. Usually the Union will claim that the Agency Fee is the same amount as regular dues, but it really should be somewhat less. If someone else hasn't already fought to get the Agency Fee reduced to 85% or so of the dues rate, then you will have to be the first to argue the case.
Unions, by Law, must represent all members of the bargaining unit, weather dues-paying members or not. That's the price they pay for being allowed to have a monopoly in representing the unit. (Normally a monopoly would be a violation of the Anti-Trust Laws and get you thrown in the slammer.) The NLRB grants Unions exclusive jurisdiction and bars any competing Unions from the worksite for three years at a time. This is a huge benefit that Unions seldom mention, or ever try to eliminate, when complaining of "free riders."
A non-Union member of the bargaining unit is, by Law, to be treated exactly the same regarding wages, benefits, representation, grievances etc. However, as a non-member he has no right to vote on contracts, or for Union Officers, or to attend Union meetings.
The National Labor Relations Board website has all this and lots more at nlrb dot gov.
Class dismissed.:D