As the case may be is typical contract language (legalese) and often redundant. In short, as the case may be means ‘depending on the circumstances’.
It is always used if there are several possible consequences or courses of action. Which consequence or course of action is relevant would depend on the actual circumstances (in the future). Semantically, the phrase …as the case may be… is used immediately after a sequence of words of which only one word is applicable to the circumstances of the contract provision. Which of the words in the sequence is referred to depends on the factual context in which the contract clause is invoked. A good example  is:
Where it appears to:
(a) a local authority in relation to any premises, processes or works, other than an activity for which a licence is required under Part IV; or
(b) the Agency in relation to an activity for which a licence is required under Part IV but has not been issued,
that it is necessary to do so for the prevention or limitation of noise, the local authority or the Agency, as the case may be, may serve a notice on the person in charge.
The use and meaning of as the case may be are similar to those of the word respectively, but certainly not the same. Similarly, the word respectively follows immediately after a sequence of words; however, respectively always links the referenced word to another word in the same contractual provision where that other word is also used in a sequence (and placed in the same order). For the phrase as the case may be it is indifferent whether it refers to something earlier on in the provision. Rather, it interacts with the actual facts or events in the reality outside the contract (and at a later point in time). Whilst respectively signals the continuation of a preceding sequence of words, the phrase as the case may be merely signals a sequence of more than one alternative, permitting the reader to apply the correct one.
It is redundant to use as the case may be as an automatic follow-up to a sequence of words, where the applicability of either of those words is anyhow arbitrary. The following use of as the case may be in the Ohio Constitution (§2.11) is therefore redundant:
No person shall be elected to fill a vacancy in the Senate or House of Representatives, as the case may be, unless he meets the qualifications set forth in…