John Dickson Carr: The Man Who Explained Miracles-Author: Douglas G. Greene-NY: Otto Penzler Books (1995)
A fantastic book. If you have any interest in Carr and his works you should pick up a copy. The bibliography at the end of the book includes information on all of Carr's work, including his novels, short stories and radioplays.
This book was nominated for an Edgar Award.

John Dickson Carr: A Critical Study-Author: S. T. Joshi-Bowling Green State University Press (1990)
There is a hardcover and paperback edition of this book. I am not sure which one was published first.
This book is, as the title says, a critical study of Carr's work. It includes a bibliography of reprints and translations.
This book was nominated for an Edgar Award.

Notes for the Curious: A John Dickson Carr Memorial Journal-Edited by Larry L. French
Carrian Press: 1978
500 signed and numbered copies were made
This is a 37 page pamphlet with contributions by Otto Penzler, Chris Steinbrunner, and others. French was working on a biography of Carr when Carr died and he wanted to "promulgate something within the year of his death, which would immediately draw attention to one who has provided so many of us so much entertainment over so many years". Unfortunately, French died before he was able to complete the biography.

John Dickson Carr, Scribe du Miracle-Author: Roland Lacourbe-Encrage (1997) in French.

A 333 page guide which contains a very complete inventory of Carr's works: novels, short-stories, summarized and reviewed by heroes, together with historical studies, radio and stage plays, movie and TV adaptations, and one of the most complete bibliography about Carr's works, including prefaces, articles and studies. It also contains a bibliographical chronology, references the names, titles, dedications and inner relations in Carr's works, and includes a list of the various parodies and pastiches of his books, plots and heroes.