Subletting an apartment is legally different from just adding a co-tenant. When you or your roommate sublet to someone else, you become landlord to a subtenant: He pays you his share of the rent and has to obey your terms as well as the landlord's. A subtenant can move in while one of you is living elsewhere for a while, or become a third roommate.
As long as your state laws and current lease allow subletting, your roommate can sublet the apartment to an individual of his or her choosing. This is true even if you are on the lease.
Rights of Roommates
If your roommate wants to sublet the apartment, she doesn't need your permission, nor does she need you to approve a particular roommate. It would be rude of her not to give you any say in the matter, but it isn't illegal. An exception would be if there's a clause in the lease that requires all roommates to approve a new subtenant. Another exception would be if you and your roommate have a written agreement giving you veto power on sublets.
Power of Landlords
Your landlord may have the power to reject a sublet. This depends on state and local law. In some cases, the landlord may place an enforceable clause in the lease barring you from subletting at all. In other instances, your landlord can approve or reject your choice of tenant.
In New York, for example, you or your roommate have to ask permission from the landlord to sublet, but the landlord can't refuse "unreasonably." If the subtenant has a bad credit history or a criminal record, saying "no" might be reasonable. If the landlord just doesn't want to sublet, that's not an acceptable reason, even if the lease says otherwise.
Possible Problems With Subletting
If you and your roommate are both on the lease, you're both responsible to the landlord for rent and for honoring his rules. Subletting doesn't change that: If the subtenant doesn't pay his half of the rent, it's your roommate, not the subtenant, who's going to be liable. If the landlord can't reach the roommate, he can demand you pay the full rent or evict both you and the subtenant.
Take Precautions When Subletting
If your roommate insists on subletting, encourage her to take common-sense precautions. Checking the subtenant's previous landlord references will reveal whether she's had problems in past rentals. Chronic unemployment could be a sign she won't be able to pay her share of the rent.
It's also smart to collect a security deposit from a subletter just as your landlord did with you. If your roommate is moving out, get her contact information and remind her she's still legally liable. When the subtenant moves in, show her the landlord's rules and any written agreements you have with your roommate, and remind her these bind her too.