Q. I seem to find conflicting information, and I can’t figure out the following: is it OK or not to introduce a block quotation with an incomplete sentence (such as “The passage states”) followed by a colon? Or does the sentence have to be a complete sentence?

A. Either way is fine. (In fact, “The passage states” is complete—or independent—on its own. “The passage states that” is incomplete.) Independent clauses usually require some end punctuation; incomplete ones often do not. Please see the examples at CMOS 13.11–21.