If you have a joint account with a partner, spouse or family member, you can still close the account using the same steps. The question of whether or not you will need the other account owner's permission depends on your state, but in general one owner can close the account without needing consent from the other owner.
However, unless you're a complete jerk, it's a good idea to give the other owner a heads up so that they can move any direct deposits or automatic payments to a different account and avoid missing a paycheck or getting charged for an unpaid bill.