It could be about both human and animal relationships, I saw components of the two. On the human side I have think that you may have been hinting at something a bit more intimate. You know, I have several pets and I've always wondered what they're really thinking so this does provide a good perspective on that subject.
P.S: One of my new kittens that I have named Frauken, (badass German names for the win!), is doing just what you described. She's asleep on my chest. For a better visual, she looks like this: http://t2.gstatic.com/images?q=tbn:ANd9GcQh5J71gNN-6GWfJ-KAyR4wR63bfYnF7_NSx8PdpJvaIvPqDzJs9A