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[i] He needn’t have told her. [epistemic or deontic]

[ii] He might have killed her. [epistemic or dynamic]

In [i] the perfect is internal in the epistemic reading (“It isn’t necessarily the case that he told her”), external in the deontic (“He didn’t have to tell her”). Similarly with [ii]: "It might be that he killed her" (epistemic), "His killing her was a possible but unactualised consequence of what he did" (dynamic).

(The Cambridge Grammar of the English Language, p204)

The latter meaning, need's deontic, is somewhat familiar to me. But I don’t find any source yet how the word, lexical need, makes the epistemic sense. Would you let me know about it?

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Here's [i] in a context which requires an epistemic reading:

1A: Amy’s found out that Ken got the promotion. Joe must have told her about it.
1B: He needn’t have told her—she might have heard it from Nancy.

Need to, as CGEL says, may be paraphrased as be necessarily true that.

Here’s a contrasting example which requires a deontic reading:

2A: Amy asked Joe whether she got the promotion, and he had to tell her that Ken got it.
2B: Oh, damn. He needn’t have told her—he could have just said it was still up in the air.

Need to may be paraphrased as be obliged to.

Both of these needs are rather formal and old-fashioned. In present-day speech they would both probably be expressed with a didn’t construction, and the epistemic sense would avoid casting Joe as the Agent:

1B: It didn’t need to be Joe who told her ...
1B: She didn’t need to hear it from Joe ...

2B: He didn’t need to tell her ...

And at least in US speech, need to itself would be much less likely than have to, in both situations:

1B: It didn’t have to be Joe who told her ...
1B: She didn’t have to hear it from Joe ...

2B: He didn’t have to tell her ...

In any case, the line between epistemic and deontic need to is fuzzy. Need to is mostly used prospectively: you need to do something in order to accomplish something else, whether that something is effecting some purpose or drawing some logical conclusion.

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