One letter, sent to Nate Shinagawa, who failed to topple Rep. Tom Reed (R), tells the Democrat that he "should be proud of your campaign and the dialogue you had with voters about the values we hold dear as Democrats."
The letter, first noticed by the New York Observer's Politicker blog, is one of at least two others, the blog reports.
The revelation that Clinton is cultivating her New York base comes as speculation over a possible 2016 presidential bid for the current secretary of State mounts.
Clinton appeared last week at the Saban Forum in Washington, D.C., a conference organized by the Brookings Institution to discuss U.S.-Israeli relations, at which she gave a speech that many observers considered a prelude to such a presidential run.
It's clear from these letters, however, that though she plans to retire from her position in President Obama's Cabinet soon, she won't be long out of public life.