In general, a right of carriage concealed or otherwise is assumed for your residence, though the individual state may mandate a license for even that type of carry. After all, the residence you put down for your CCL is your domicile, be it house or apartment.
However, when dwelling in an apartment, you must also comply with the rules of the landlord in order to a. not violate the law (since carry on private property against a landowner's wishes is armed trespass) and b. not violate your lease, which would be unfortunate. If your state allows carry in the residence without license, or if you have a state carry license, just check your landlord's rules and regulations, and review your lease. If you are still not sure, look for obvious signs on the property or ask the landlord.
When travelling outside the four walls of your apartment, you should have a CCL (unless you live in Vermont or carry openly). Even though it is private land, and even if you have the permission of the owner to carry, if you carry concealed and accidently step foot onto public land or a public right of way, you could be breaking the law. For instance, even though I live in an apartment complex, the dumpster is across a public access street, so when I take out the trash, I always carry my license.
It has been my experience that landlords actually like CCL holders, but your results may vary.