In a statement, the state police said multiple state and local lawmakers reported receiving the email.
ABC affiliate WTEN-TV first reported the email, which included the subject line "Time to Kill."
The writer says, "News reporters, politicians and the wealthy are all going to be targets."
The message was sent from someone using the e-mail address email@example.com.
The writer makes references to the state budget and attacks on labor unions and criticizes budget protesters as "fools marching around the Capitol and taking orders from the State Police."
"I personally am going to use my position and contacts in State government to gather information about the vulnerabilities of public and private targets in New York," the writer said.
A New York State Police spokeswoman would not comment to ABC News on whether security had been enhanced for leaders of the legislature.
The writer adds, "Understand with whom you are dealing. I am not a crazy. I am a terrorist. I stand for all the people who don't have a voice."
In the final paragraph, the writer refers to speaking to a legislator three years ago and warns: "I bet he wasn't paying attention. We're going to get his attention. Come visit my agency. Give me a chance to pull a Gabby Giffords."
READ MORE ON ABCNEWS.COM: http://abcnews.go.com/Blotter/york-legislators-threatened-attack-gabby-giffords/story?id=13277840