Employees of the federal government by law are guaranteed the right to refrain from joining or assisting a union. See (federal employees generally); (postal employees). (U.S.C. stands for "United States Code.") This means that you have the right to resign from union membership, and stop paying dues.
The decision to resign or not is wholly yours. As a nonmember you would not be subject to union rules and discipline. The union would have to continue to represent you fairly and without discrimination in all matters subject to collective bargaining, contract administration, and grievance adjustment, and you could not be denied any benefits under the labor contract with your employer because of nonmembership. On the other hand, you would not have the right to vote on ratification of the contract or election of union officers, and there may be benefits provided under the union's constitution that are not available to nonmembers.
You can resign by simply submitting to your union a written letter stating that you are doing so. If you have authorized payroll deduction of your dues, you would also have to notify your employer that you wish to revoke that authorization. If you signed the authorization less than a year ago, or if it renews automatically each year, revocation may not be effective until the end of the current authorization year. It is advisable to obtain a copy of your payroll authorization and review it.
If you decide to resign, and your union or employer refuses to honor
your resignation, you would be entitled to file unfair labor practice charges against them with the Federal Labor Relations Authority (federal employees generally) or the National Labor Relations Board (postal employees only). However, you should be aware that claims concerning conduct that occurs more than six months prior to the filing of charges may be time barred, so it is important to pursue claims promptly.