What 2012-2015 SCOTUS decisions make "letter[s] from the grave" inadmissible into evidence?

Question

I've read this interesting bit:

In a 2008 trial where a man was accused of poisoning his wife with antifreeze, Schroeder allowed into evidence a letter the wife wrote a neighbor accusing the husband should anything happen to her. The so-called "letter from the grave" evidence proved key to conviction. Wisconsin's Supreme Court this year ordered a new trial for the man and ruled the letter should not have been admitted as evidence.

Schroeder sentenced the defendant to life in prison without a chance of parole. Before announcing his sentence, Schroeder told the defendant: "Your crime is so enormous, so monstrous, so unspeakably cruel that it overcomes all other considerations."

I have tracked the case to its Wikipedia page but from a quick read of the latest decision in this saga, it's not clear why the Wisconsin Supreme Court has decided the evidence was inadmissible... other than them saying

The State asserted, as it does on appeal, that United States Supreme Court cases decided in 2011, 2012, and 2015 modified the definition of what constitutes a “testimonial” statement and that under the revised definition, Julie’s letter and other statements do not qualify. The circuit court agreed and ruled that the letter and statements are nontestimonial and could be admitted at trial. The State subsequently filed a motion to reinstate the original jury verdict without a retrial, and the circuit court did just that, reinstating the original conviction as well as Jensen’s life sentence, explaining that there was no need for a new trial because the evidence would be “materially the same as the first trial.” Jensen appeals.

Somewhat strangely for a legal decision, the exact SOCTUS cases don't seem explicitly cited. The decision mentions the Confrontation Clause; upon looking at the Wikipedia article on the latter... two 2011 cases are mentioned (one of them rather confusingly summarized, IMHO):

[In] Bullcoming v. New Mexico, 564 U.S. 647 (2011), the Court ruled that admitting a lab chemist's analysis into evidence, without having him testify, violated the Confrontation Clause. In Michigan v. Bryant, 562 U.S. 344 (2011), the Court ruled that the "primary purpose" of a shooting victim's statement as to who shot him, and the police's reason for questioning him, each had to be objectively determined. If the "primary purpose" was for dealing with an "ongoing emergency", then any such statement was not testimonial and so the Confrontation Clause would not require the person making that statement to testify in order for that statement to be admitted into evidence.

So what were the 2012 and 2015 cases?

Answer 1

The general problem with a "letter from the grave" is that it violates a defendant's rights under the Confrontation Clause. The major decisions interpreting the Confrontation Clause from the years in question are:

• Michigan v. Bryant, 562 U.S. 344 (2011) (holding that the Confrontation Clause does not prohibit the introduction of hearsay statements whose primary purpose was to address an ongoing emergency)
• Williams v. Illinois, 567 U.S. 50 (2012) (holding that the Confrontation Clause does not prohibit expert testimony as to hearsay statements assumed to be true for purposes of informing her opinion)
• Ohio v. Clark, 576 U.S. 237, (2015) (holding that the Confrontation Clause does not prohibit the introduction of hearsay statements that "were not made with the primary purpose of creating evidence")