The character is inspired by Robert Durst:
It takes barely any time at all for Netflix’s Unbreakable Kimmy
Schmidt to offer up one of the best gags of its second season: A
recurring appearance from infamous true crime subject, Robert Durst.
Only, it’s not Durst, but SNL alum Fred Armisen’s spot-on impression
of the Durst presented to the world in HBO’s 2015 series, The Jinx.
The docu-series about the self-admittedly homicidal billionaire
eccentric quickly captivated the country last February and March, with
Durst mania reaching its height at the tail end of the spring, just as
the writers of Kimmy began to discuss season two.
“In and out of that summer, obviously, everyone was just obsessed with
The Jinx when we sat down to write,” co-creator Robert Carlock says
between chuckles, as if he knows full well just how absurd Armisen’s
cameo truly is. [...]
Durst initially pops up as a former flame of nutjob landlady Lillian
(Carol Kane), but his role takes on a bigger shape in the season when
the two rekindle their romance over roller skates and ukulele duets.
The biggest champion of introducing Durst as a love interest for Kane
was Carlock’s co-creator, Tina Fey. “Tina really insisted that the
overlap between these two New York eccentrics, as one might term them,
was just too good,” says Carlock. “And I think Lillian has a very high
level of tolerance for violent eccentricities.”
I suspect the use of the ukulele is merely a device to display the character's eccentricity.
It should be noted that Vulture also noticed the similarity:
Not many shows would make the call to wrap up a season premiere with a
Jerk-meets-Jinx ukulele duet in a roller rink, but in Kimmy Schmidt's
weird world, that's par for the course. Pretty damn hilarious, too.