Nafissatou Diallo brought the action after criminal charges were dismissed against the former head of the International Monetary Fund (IMF).
The charges were dropped when prosecutors lost faith in her evidence.
Dominique Strauss-Kahn is not in court. He is fighting claims in France that he was involved with a prostitution ring.
The hearing in New York is the first stage in the civil case brought by Nafissatou Diallo.
Nafissatou Diallo maintains DSK attacked her when she came to clean his suite at the Sofitel Hotel in New York.
Judges must decide whether the case can proceed.
DSK’s lawyers argued in court that the case should be dropped, saying the defendant had diplomatic immunity at the time of the alleged assault.
“Dismissal, your honor, may seem like an unfair result to some, but it’s the result the law compels,” Amit P. Mehta, one of DSK’s lawyers, told the judge.
But the IMF has said Dominique Strauss-Kahn was not entitled to immunity because he was in New York on personal business at the time.
In France, DSK has been placed under investigation over allegations that he was involved in a hotel prostitution ring in the northern city of Lille.
DSK has admitted he attended sex parties, but denies that he knew the women involved in the orgies were hired prostitutes.
Leaked police documents emerged on Wednesday that appear to show that he exchanged text messages with the people running the parties, in which prostitutes were referred to as “material”.
Prosecutors claim the term suggests he knew the identity and profession of the women taking part.
At least one of those women has told police there was undue aggression at these events, an allegation Dominique Strauss-Kahn strenuously denies.
The parties DSK attended were stopped soon after his arrest in May last year.
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