Charlie – “Sanhedrin 57a, and Rambam Hilchot Melachim 9:14 require an eyewitness to the crime.”
I took a long time to answer because I wanted to look at the Sugya(s).
I understand where you are coming from but let me try to explain my perspective. The Rambam says that a Goy can’t be an Eid acc. to the Torah. So how does this coincide with the fact of -you need one Eid (even a Goy) to testify in the Goyishe courts? You might have a different Teretz, but I’m learning that Eid doesn’t mean only an Eid but any evidence that the crime has occurred. Their testimony isn’t believed because they are an Eid, but because they are revealing to us what happened. Similarly if we know from evidence that this is what occurred, the court would have to find the perp guilty. So IMO, circumstantial evidence has to be accepted in the Goyishe courts.
The question would remain can Bais Din implement Kipa in such a case? From the Gemorrah & Rambam on Kipa, I’d venture to say -yes. Because the Gemorrah asks if there are no Eidim that he committed a crime -how do we know he did it? So the Gemorrah gives a few Tirutzim, which acc. to the Rambam all apply. The Meforshim say one Eid wouldn’t work because it’s just Loshon Horah. (Another possible Rayah that the Goy isn’t believed in Goyishe courts because of Eidus.) But from the Gemorrah’s Kasha it is Mashmah, if we have other ways of knowing like for example circumstantial evidence or perhaps something like DNA evidence we would be able to use these to put him in a Kipa. And it’s not a Kasha why circumstantial evidence wasn’t mentioned because you see each Amora who did mention something didn’t mean it to exclude something else (Rambam), so it’s quite possible that there are other ways of killing with “No Eidim” that a perp would be sentenced to the Kipa.