Fri Forgotten Books: The Mystery of Central Park, by Nellie Bly (1889).

He was questioned why he used the definite article instead of the indefinite in answering the officer's question.
—Nellie Bly, The Mystery of Central Park

In The Mystery of Central Park, lazy man-about-town Richard "Dick" Treadwell must prove his worth to prospective fiancee Penelope (and clear his name) by discovering who killed a young woman in Central Park. Dick finds that he is being followed as his investigation leads him into less savory areas of New York. Bly's interest in portraying the plight of the working class is evident in Dick's acquaintance with pretty factory worker Dido and her friends who are deprived of a living wage (a relationship not regarded with favor by Penelope).

"Penelope, with calm but serious face, kept close to the
morgue-keeper." Illustration from The Mystery of
Central Park by Nellie Bly. New York World,
19 July 1889

The modern reader will find it hard to give credence to Dick's chance discoveries of information that prove so crucial to the case, and those with even a passing acquaintance with forensics will loathe the fact that Dick is permitted to take the dead woman's clothes from the morgue (although his reason for doing so shows some logic). The portrait of the Pygmalion-like murderer has some elements of interest. The Mystery of Central Park should perhaps be regarded as a curiosity of a famed journalist's career and a continuation of her focus on progressive issues rather than as a significant contribution to the mystery literature.

Nellie Bly, ca. 1890.
Library of Congress,
Prints & Photos Div.

The intrepid Nellie Bly (aka Elizabeth Cochrane Seaman, 1864–1922) became a reporter at age 16 and made her name as a "stunt" journalist, accomplishing a celebrated around-the-world journey in 72 days (meeting Jules Verne along the way and beating the 80 days of his character Phileas Fogg) and arranging her commitment to a mental asylum so she could write about the treatment of the mentally ill (see Ten Days in a Mad-House, 1887). The Mystery of Central Park was her sole mystery novel.

There are only three copies in U.S. libraries of the book version of The Mystery of Central Park. I found the serialized version in the New York World and have uploaded the parts as a resource for readers:

• Parts 1–4
• Parts 5–8
• Parts 9–12 

Update, 6-11-13. The Library of Congress has digitized its copy of The Mystery of Central Park (available at the Internet Archive).