Adding an additional wrinkle to the situation, there was an electrical line running from the distribution pole in the backyard through the crotch of the cat's limb on its way to the street light up front. This was only a single, insulated line that powered only the street light, so it was not nearly as dangerous as an uninsulated distribution line, but it still had plenty enough current to kill if the cat or I should touch the wire if it had been exposed by frequent and long-term rubbing against the tree on which it was resting. Fortunately, the wire was in good shape, and the insulation appeared to be completely intact.
He rubbed his face on the limbs, and he sniffed my hand and let me pet him. Several times, he reached out a paw to touch my hand in a cute way that I have not seen before. As we established our friendship, we both relaxed and felt relief that the troubles we had earlier feared were no longer a concern.
Now that he trusted me, he stepped down into the crotch to get closer to me and rested there on top of the electrical line. He then began to rub his face across the wire. No harm was done, thanks to the intact insulation. As he sat there facing me, it appeared that he would like to step onto my lap, so I began to encourage it. He calmly stepped down on my lap, and I pulled him in close to my body. I smiled and marveled at the difference between this outcome and the trouble I had expected when I first began to climb up to him. I brought him down as gently as I could, and when we reached the ground, he jumped down from my lap, walked away a few steps and then returned to me as if to say, "thank you."
Now that he was safely on the ground, he was ready to eat. Some food was already there on the ground waiting for him, but I gave him the food I had offered him in the tree, and he ate from both. While he ate, I petted him some more and also looked at him more closely and scanned him for a microchip. No chip was found, but now I could see that he was a neutered male.
Normally, when I get a call to rescue an unknown cat, I always ask the caller or the immediate neighbors to be responsible for the cat until its owner can be found. Sometimes, however, that is not possible, and that was the case this time. Since the cat did not have a collar or microchip, I checked for online posts for lost or missing cats but did not find one matching his description. Since he was neutered, appeared in very good shape, was very friendly and affectionate and had been seen many times before in the neighborhood, I decided it was safe to assume that he belonged to someone nearby and would find his way back home. I have never turned a rescued cat loose before, but it seemed to be appropriate this time in spite of the guilt I felt as I did so. I hope I did the right thing.