sheet2json.gs

function doGet(e) {
  var params = e.parameter;
  var sheetName = params.tabname || undefined;
  var sheetId   = params.sheetid || undefined;
  
  if (!sheetName || !sheetId) {
      var json = {
      error: 'Missing or incorrect values for parameters: tabname || sheetid'
      };
  } 
  else {
      var book = SpreadsheetApp.openById(sheetId);
      var sheet = book.getSheetByName(sheetName);
 
      var json = convertSheet2JsonText(sheet);
  }
 
  return ContentService
          .createTextOutput(JSON.stringify(json))
          .setMimeType(ContentService.MimeType.JSON);
}

function convertSheet2JsonText(sheet) {
  // first line(title)
  var colStartIndex = 1;
  var rowNum = 1;
  var firstRange = sheet.getRange(1, 1, 1, sheet.getLastColumn());
  var firstRowValues = firstRange.getValues();
  var titleColumns = firstRowValues[0];
 
  // after the second line(data)
  var lastRow = sheet.getLastRow();
  var rowValues = [];
  for(var rowIndex=2; rowIndex<=lastRow; rowIndex++) {
    var colStartIndex = 1;
    var rowNum = 1;
    var range = sheet.getRange(rowIndex, colStartIndex, rowNum, sheet.getLastColumn());
    var values = range.getValues();
    rowValues.push(values[0]);
  }
 
  // create json
  var jsonArray = [];
  for(var i=0; i<rowValues.length; i++) {
    var line = rowValues[i];
    var json = new Object();
    for(var j=0; j<titleColumns.length; j++) {
      json[titleColumns[j]] = line[j];
    }
    jsonArray.push(json);
  }
  return jsonArray;
}