I've had to deal with a few problems over the years and know of a few dodgy people in the area.
I've found a suspicious dead own on my woodland about this time of year but when I looked into it it is not uncommon. Young owl fledglings can struggle to feed themselves and with the recent poor, wet, weather may starve to death.
I'd look closely at the remains and see if there was anything in them. If someone has shot it I would guess unlicensed air rifle or catapult as I don't think owls tend to be persecuted.
You could raise it with your local police wildlife crime officer, one I've met was very knowledgeable, but I've also dealt with other police (as a witness) who left a lot to he desired. Or a local owl charity.
It would be worth getting to know your neighbours as they may well know what goes on in the area, legal or otherwise.