I read this book when I was a teenager, or in my early twenties, so that puts it no later than 1979. My favorite authors at the time were (of course) Asimov, Bradbury, Clarke, Heinlein, and a few others. I've looked up the bibliographies of most of these, to no avail.
The story in general: Earth people spot a small alien craft near the sun. Investigating, they find a lone passenger, a female pilot from an alien race, whose distinguishing characteristic is that her hands are claws of two different sizes: one large, one small. She is suspiciously quiet about how she got there (I think). Examining the video footage, they find that, as the Earth ship approached, she jettisoned four other passengers into the sun.
There is much talk about sexual practices (which makes me think Heinlein). Earth society is going through another "sex is sinful" stage, but the alien female has a biological imperative to breed; if she doesn't have sex, she'll die. Since her shipmates are gone, she keeps getting sicker.
They return her to her own world, and find that there are five different races, all of which build a fully-integrated society. The creatures are of different size, shapes and colors, but all have the same mismatched claws. One breed of alien is like a technician, and, for example, while waiting outside by the car (which are a story in themselves), he or she uses the larger claw as a tool to repair, upgrade, or modify the vehicle. All of the aliens are capable of things like this, so there are no businesses to take care of it. Basically, everyone does everything, if I recall correctly.
I don't remember the resolution of the story, and probably for that reason it's been bothering me for several months. If this sounds familiar to anyone, please let me know the title and author, and if I can download a digital copy somewhere.