When to drop "dass"

Question

Under what circumstances can/do you drop "dass" in German? Is it similar to the usage of "that" in English. (The links below outline what I mean by that for those of you unfamiliar.)

Examples:

Sie hat gesagt, sie weiß es schon.

Er hat erklärt, dass er zu neuen Verhandlungen bereit ist.

Links:

https://english.stackexchange.com/questions/296720/what-does-the-complementizer-that-accomplish-in-terms-of-style#comment666016_296720

https://english.stackexchange.com/questions/307438/should-i-use-the-word-that-in-a-sentence-when-it-is-not-required

Also, note that the answer to the question pasted below only discusses how one would use formal language instead of the "dass." The examples above are (fairly?) colloquial so I don't think this question should be marked as a duplicate.

When does one require "dass" and when can it be omitted?

Answer 1

You cannot omit dass, ever.

Your example shows two different constructions; the one with dass uses a subclause, and if you want this kind of subclause you must mark it with dass. For some verbs such as "sagen", you can use a subordinated main clause, which doesn't use dass, but as Carsten points out, that isn't just dropping the dass, it also involves using a different sentence pattern with a different word order.

You can only ever omit dass in parallel constructions with a coordination. For instance both, the following are correct:

Sie hat gesagt, dass sie es schon weiss und dass ich sie nicht nerven soll.

Sie hat gesagt, dass sie es schon weiss und ich sie nicht nerven soll.

However, this is a general property of coordinations: repeated elements in the same positions can be omitted; it has nothing to do with dass in particular.

Note that in English, the word that can sometimes be omitted when it's an object relative pronoun (and in older dialects it could be omitted even as a subject relative pronoun). This effect doesn't translate to German, since German uses der, die, das as relative pronouns and not dass, and they cannot be omitted.