They were known to be together. They had a fraught relationship (already stated by parents).You need to prove it beyond reasonable doubt. There is no evidence. You are basing this on suspicion.
They were spoken to by the police because of physical abuse.
One gets strangled. There is no one else around.
One returns home in the other's vehicle, unaccompanied.
Then subsequently refuses to speak about the other (allegedly).
What sort of evidence should there be? What doubts would you have?