harrykthaw

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.

On the way to or from his July, 1915 sanity trial, where he was adjudged sane.
en.wikipedia.org/wiki/Harry_Kendall_Thaw
See notes under

Thanks for pointing out the related photo and the context! We'll add information to the description when we next update it.

Probably also more men who had something to do with the Harry Thaw escape conspiracy trial. William Gordon was a hotel proprietor who testified that the defendants stayed at his hotel before the escape. His nephew, Gordon Dike, also testified. select.nytimes.com/gst/abstract.html?res=F20D15FC395B1773... The other two I'm not sure about. One of the defendants was Michael O'Keefe not William but maybe the label is wrong.

Another shot of William Gordon: