Get a roofer in to go round the roof to check whether there is anyway obvious he got in. If your house is a semi or terrace, get the roofer to look in the roof to check whether it got in via next doors house.
Grey squirrels got into our roof, ate through the alarm system and stripped 2 foot of plastic sheathing off an electricity cable, which could have caused a catastrophic fire. We discovered that they got into our house through a gap in the loft wall with next door. Once we blocked that the problem has not re-occurred.
Squirrels are just rats with tails, who have passed diseases on to red squirrels and wiped them out over most areas of the country. I wouldn't want to have one shot in the house. Usually they take them away in a trap and kill them humanely elsewhere.