this happened to a woman I used to work with. She wanted a tree in her front garden lopped but thought she should check if there was a TPO on it. She called the Council who came and said there wasnt but then slapped one on it. she was livid! So, see if you can search without alerting the officials
If you look on your council website you should find the number of the relevant department. In mine it is part of the planning department. They look up a database so the chance of them coming round to look atyour tree and slapping a TPO on it is pretty slim unless they are very underworked.
Having worked in a planning department, ring your local council. The planning department will have the appropriate records. You may be able to visit the offices, and do the search yourself. Even if it has aTPO you can make an application ofr work to be carried out. The tree officer should be able to advise you. A good prune may make it safer, but a genuine risk to your property sould be sufficient grounds to fell it.