Style guides can vary on what is required in the text itself--not just the actual citation. Be aware of differences, particularly with regard to formatting quotations.
The Bluebook (Rule 5.3(a)) and Chicago (Rule 13.50) agree that beginning and ending ellipsis points shouldn’t be used when using quoted language as a phrase or clause, even if matters are omitted before and after the portion of the quotation being cited.
Compare The Bluebook 5.3(b) and Chicago 13.50-51 with regard to using quoted language as a full sentence.The Bluebook has stricter requirements with regard to bracketing changed capitalization and requires ellipsis points at the end of a quoted sentence, unlike Chicago.