Open check in form with JQuery

There is a CheckInFile web service operation. If you are using the SPServices library, there is an operation for that (copied from the documentation):

// Check in a single document, disable all of the column controls and give a visual cue that it is checked in
 function checkInDocument(obj, pageUrl) {
  var success = true;
  $().SPServices({
   operation: "CheckInFile",
   async: false,
   pageUrl: pageUrl,
   comment: "Checked in during bulk upload",
   CheckinType: 1,
   completefunc: function (xData, Status) {
    $(xData.responseXML).find("errorstring").each(function() {
     alert($(this).text() + " Please save all of your changes before attempting to check in the document.");
     success = false;
    });
   }
  });
  // If we couldn't check the document in, then don't disable the item's row
  if(!success) return success;

  return success;
 }