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.

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.

As a native speaker of English, I consider "that've" to be a perfectly valid word. Grammarians be damned!

I definitely use it in spoken English (native of the United Kingdom) and have heard it used often here. I've never seen it written that I can remember. Google books search doesn't find much and the Google Ngram search only brings up a very small number.