If the lawyer filling out the Case Information Statement makes a mistake, or if circumstances change or new information is discovered, the party wishing to amend the statement may do so by making a motion to the judge in charge of the case.
For example, the equivalent document in federal district courts is Form JS-44, Civil Cover Sheet.
Similarly, the Superior Courts of California have a Form CM-010, Civil Case Cover Sheet.
Questions typically asked on Criminal Case Information Statements include: New York's equivalent document is the Request for Judicial Intervention, which is necessary because in New York a case begins with the service of a complaint after filing with a local County Clerk.
Thus, a New York Supreme Court Justice's involvement in a case will not take place until absolutely necessary (usually because a discovery dispute develops, someone wants to file a dispositive motion, or it is actually time for trial).