Women don't kill by ligature strangulation. Can you find any example where a woman has done that? I spend a lot of time following crime-solving and forensic shows and web sites, and I can't recall a single instance of a woman comitting a murder using ligature strangulation.
"Women don't kill by ligature strangulation."
There's always a first time. However, here is how I see it having gone down. Patsy, in a fit, clobbers her kid over the head with a flashlight, mortally wounding her or outright killing her. Patsy's husband John does the ligature to cover up what actually happened. Or, in the alternative, they were both in on it together. But I believe Patsy was the prime mover here, and John Ramsey knew exactly where to go to "find" his daughter's body in the basement. No one entered that house. Either Patsy, her husband, both, or their son (highly unlikely) are the perpetrators. This was not an outside job, it was an inside one. All fingers point to Rome. The police have always maintained their air of suspicion towards the Ramsey family as the perpetrators. We'll probably never know the exact how of it, but at least one-half (and perhaps) the sole perpetrator of the death of their daughter now lies in a grave next to her victim.