I think you are but I am no lawyer. Here in Ohio I have the right to remove branches hanging on my property but have to pay for the removal. I just had this done for safety‘s sake over our driveway. But happily my neighbor offered to pay for it. Good luck!

You can trim limbs over hanging your property. Your insurance will pay for any damage should they fall since it will be considered “an act of God”; unless you have documented sharing this concern with your neighbor and the tree exhibits signs of that type of failure.

Whatever you or anyone else does, Check with authorities to be sure, very sure the power is off before attempting any kind of branch removal or maintenance.

If you can visually confirm that the tree has no lines touching it, even lines that are on the ground can kill you, otherwise you should be okay.

If the tree's owner knows or should have known of the impaired condition to his tree, he is responsible to correct it. Send him an E-mail with photo attached - CC your insurance.

What does your neighbor have to say? If they are big enough to cause damage, they may be too big for a safe, quick DIY. Maybe your neighbor is trying to get quotes but due the recent storms, most reputable tree service companies are very busy.

Is email an acceptable way of doing this?

At one time it had to be a registered letter.

Use E-mail!