harrykendallthaw

en.wikipedia.org/wiki/Harry_Kendall_Thaw

Actually, not the courthouse, but instead the photo was taken in front of the Ludlow Street Jail, no longer standing. The sign by the front door reads "New York County Jail" (New York County is essentially Manhattan), and that is what the Ludlow Street Jail was.
Thaw, in 1915, was returned to New York City after escaping confinement at Matteawan State Hospital (He had been acquitted of the 1906 murder of architect Stanford White by reason of insanity). His lawyers successfully asked the court to move him from The Tombs to the Ludlow Street Jail, on the basis that he was not charged in a criminal matter, but that he was to have a jury trial only as to his present sanity.
query.nytimes.com/gst/abstract.html?res=F10916F93E5D16738...
In this old print, you can see that the door was near the corner of Ludlow and Essex Market Place. [Essex Market Place ran from Essex to Ludlow Streets between Broome and Grand Streets and was closed in 1926, around the time the jail was demolished.] You can see that there was a giant gas lamp over the door, whereas in Bain's 1915 picture just the bracket remained.
digitalgallery.nypl.org/nypldigital/dgkeysearchdetail.cfm...

knickerbockervillage.blogspot.com/2009/10/seward-park-aer...

This was probably taken when Thaw was due to be taken from the jail to court.
He and 5 others who helped him escape the state hospital were tried in March, 1915 and acquitted. He then had a second trial in 1915 to determine if he was presently sane. He was determined sane in this trial on July 14, 1915, which is presumably about when this shot was taken.
The New York Times account describes 2,000 people gathered at the courthouse, cheering thaw after the trial:
query.nytimes.com/gst/abstract.html?res=FA0E10FC3E5A15738...

See also:

And not to forget, the Thaw trials were about Evelyn Nesbit Thaw, or more exactly Thaw's shooting of her presumed lover, Stanford White.

Harry Kendall Thaw fled to Canada in 1913. William Lewis Shurtleff was his lawyer for the extradition at this courthouse. Thaw had murdered Stanford White because White had had sex with Evelyn Florence Nesbit before she became Thaw's wife. Nesbit at the trial described the intimate relationship with White including the velvet swing he kept in one of his apartments. The story was fictionalized in Ragtime.

Husband of Evelyn Nesbit, murderer of Stanford White, a repeat appearance on the LoC stream...

www.flickr.com/photos/masha_ma/4694145136/

[When the photo was taken, Thaw was freezing . . .] Having escaped from a New York insane asylum in 1913 and fled to Canada, Harry K. Thaw, the murderer of Architect Stanford White, was extradicted back over the border to the U. S., then spent several months in limbo in Concord, New Hampshire, resisting return to New York for a trial on escape charges. He finally was hauled back to NY on January 23, 1914. In 1915 he was judged restored to sanity, and let off scott free. Another Bain/LOC photo of Harry Thaw, in the sheriff's office in Concord, NH (Click on the photo for further links and text):

Poor Evelyn Nesbit.