Whether, or under what circumstances, a criminal defendant who opens the door to responsive evidence also forfeits his right to exclude evidence otherwise barred by the Confrontation Clause.
As the petition says, “[a]ll agree that a criminal defendant, like any other litigant, may open the door to the admission of evidence that is otherwise inadmissible under the ordinary rules of evidence when it clarifies, rebuts, or completes an issue” that the defendant has raised. But that’s under the “ordinary rules of evidence,” e.g., the rules regarding hearsay. What about constitutional rules of evidence like the Confrontation Clause? Does a defendant forfeit its protections simply by raising factual “issues” that otherwise-excludable statements might bear upon?
Per the petition, a smattering of courts are divided on this question. A few have held that a defendant never “opens the door” to confrontation violations: the confrontation right is not “subsumed by  evidentiary rules.” United States v. Cromer, 389 F.3d 662, 679 (6th Cir. 2004). A few others have held that a defendant may open the door where he or she introduces part of a testimonial statement that would otherwise be excluded: the rule of completeness or general equitable concerns then permit the government to introduce the rest of that statement – nothing else. See United States v. Moussaoui, 382 F.3d 453, 480-82 (4th Cir. 2004)
Then you have three jurisdictions like New York, the respondent here. They hold that the government may introduce testimonial hearsay any time it’s useful to correct a “misleading” impression created by the defendant. The facts in this case are tough to summarize; suffice to say that “misleading” in this context is a rough synonym (as in so many contexts) for “inconsistent with the prosecution’s version of events.” Stay tuned; we’ll see if SCOTUS thinks the confrontation right protects only those defendants who are not so rude as to put on a defense. (SCOW has before it a case raising a similar question about Miranda; see here and here.)