What type of case? Generally, the court does not appoint attorneys is civil court cases.
I am a former federal and State prosecutor and now handle criminal defense and personal injury/civil rights cases. Feel free to check out my web site and contact me at (212) 577-9797 or via email at Eric@RothsteinLawNY.com. I was named to the Super Lawyers list as one of the top attorneys in New York for 2012. No more than 5 percent of the lawyers in the state are selected by Super Lawyers. The above answer is for informational purposes only and not meant as legal advice.
Legal aid organizations exist which may take on representation in civil matters sometimes for defendants who have no money. Typically there are many more people who want such representation than the legal aid organization can afford to represent. I know of no right to representation by counsel in civil matters. Sometimes a lawyer will take on a civil matter for a defendant who has no money on a pro bono basis, but one cannot count on finding such counsel.
Good luck in your search for representation.
Not legal advice as I don't practice law in New York. It's just my two cents. If you need legal advice, consult New York counsel. I practice in Vermont ONLY.
The court won't appoint an attorney in a civil case. If you meet specific income requirements you might find assistance at Legal Aid or a law school with a clinic.
For a free consultation related to medical malpractice, personal injury, workers' compensation, social security disability or nursing home abuse, please contact Lowenthal & Abrams, PC at 1-800-876-5299. I am licensed in Pennsylvania, but members of my firm are licensed in Pennsylvania, New Jersey and New York. This post is not legal advice, but instead contains general educational information. Please do not act or refrain from acting based upon what you read in this post. Also please remember that this post does not form an attorney/client relationship between you and me. If you have specific legal questions, you should contact an attorney in your state for assistance. I am licensed to practice law in the state of Pennsylvania.