Is "that've" a valid contraction for "that have"?

Is "that've" a valid contraction for "that have"?

For example, the sentence: "I've been working with some substances that've been detrimental to my health."

It follows the patterns of other similar contractions (like would've, that'll've, and others), but doesn't seem to be any dictionary I could find.

Answer

It's certainly found in speech alongside who've and which've, and that's how the pronunciations are normally represented in writing. It's a matter of judgement whether you use them in writing when not reporting actual speech, depending on the degree of formality of the context.