One copy is filed. However, it is always a good idea when you are commencing the case and filing the Summons or Summons with Notice to bring and have multiple copies stamped for your own records, and use later when filing the final packet of papers. As for the final packet, file one copy but make sure you retain a set of the papers for yourself so that if there is a problem, you have your copy to refer to.
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One to be filed. Bring an extra copy and have the clerk time stamp it so you can serve the Summons and Complaint. Make sure you write the index number on the summons and complaint before you send it out for service.
File the original summons and verified complaint with the Court and have another stamped by the clerk's office. Keep an additional copy or two for your own file. If you are referring in your question to a completed submission packet, you need only file one complete set, but remember to include 1 Note of Issue with 2 additional copies.
The foregoing information should not be construed or relied upon as personal legal advice or creating any attorney-client relation but merely as a comment or discussion only to a posted inquiry.