I've only just seen this thread, and want to say how upsetting this must have been for you Willow10 - but he is a bully and is wanting a reaction.
Well, the best reaction is to inform the police as you have done and send a copy of his letter to the Council Planning Department too.
You are not the only one to object to the tree felling so I hope all your neighbours who also objected are aware of his bullying tactics.
The tree is old and has a TPO so you did the right thing to object. I doubt he will win unless it is in a dangerous state and liable to fall and cause damage.
In our area all comments on any planning proposals are available freely for anyone to see online, letters, emails etc are published in full.
Some time ago we were sent a notification that our neighbours wished to build on a plot of land next to them and we wrote to say we had no objections (it would not affect us much). However, another neighbour objected most strongly, saw our letter online and accosted DH in the street, using foul language and calling us both rude names.
Incidentally, they didn't get permission because of a tree with a TPO on it!
We just ignored it and he didn't speak to us for quite a long time!