It depends on what you mean by “merging.”  If there is a true merger of the two organizations, one of them, presumably the larger statewide organization, will be the surviving entity and the other will cease to have a separate existence and will disappear.  There won’t be anything left to retain the 501(c)(3) exemption.

If, on the other hand, the board of the statewide organization takes over and becomes the board of the local organization, or the statewide becomes the sole member of the local organization, there will still be a separate local organization with its own exempt status.  It may be easier to raise local contributions for the local organization than for the statewide one, but I think the more important question is about the type of “merger” that makes the most sense.  If the local corporation remains as a separate legal entity, it will keep its exemption.  If it merges out of existence, it won’t.  (See Ready Reference Page:  “Mergers and Acquisitions Can Take Many Forms”)