So it seems we're both right -- the first edition with some material from the later editions missing, is indeed in the public domain. But on the U.S. Copyright office web-site, a search does show that this book is copyrighted. Apparently it's the later edition with the extra material, though.
My apologies to Patricia for my hasty reply -- I just don't want this forum to get in trouble with the copyright police and get shut down.
I really enjoyed the later edition (still copyrighted) with the additional material which helps to better understand the later books, since it provides more insights into Lord Peter's family. And the later edition with the extra material is still under copyright in the U.S.
Thanks for pointing me to the place which states (hopefully correctly) that this is indeed a public domain book.