Revision 9c8c7527-86f5-4eba-b6fd-a85df1eac4f1

You can overide some css style to achieve the result you want ,
by changing `height` , and `overflow` properties to rendered menu item as flow

    .dojoxCheckedMultiSelect .dijitMenuTable {
      /* fix some rendering issue menu item width table*/
      width: 100%;
    }
    
    .dojoxCheckedMultiSelectMenu {
      /* set scroll-x to scroll and hide y scroll bare*/
      overflow: hidden scroll !important;
      /* set max height for dropdown menu */
      max-height: 150px !important;
    }


You can check working snippet here :

<!-- begin snippet: js hide: false console: false babel: false -->

<!-- language: lang-js -->

    require(["dojo/ready", "dojox/form/CheckedMultiSelect"], function(ready, CheckedMultiSelect) {
      ready(function() {
        console.log("Hi");

      })

    });

<!-- language: lang-css -->

    html,
    body {
      width: 100%;
      height: 100%;
      margin: 0px;
    }



    .dojoxCheckedMultiSelect .dijitMenuTable {
      /* fix some rendering issue menu item width table*/
      width: 100%;
    }

    .dojoxCheckedMultiSelectMenu {
      /* set scroll-x to scroll and hide y scroll bare*/
      overflow: hidden scroll !important;
      /* set max height for dropdown menu */
      max-height: 150px !important;
    }

<!-- language: lang-html -->

    <link href="//ajax.googleapis.com/ajax/libs/dojo/1.10.0/dijit/themes/claro/claro.css" rel="stylesheet" />
    <link href="//ajax.googleapis.com/ajax/libs/dojo/1.10.0/dojox/form/resources/CheckedMultiSelect.css" rel="stylesheet" />

    <script>
      dojoConfig = {
        parseOnLoad: true,
        async: true
      };
    </script>
    <script src="//ajax.googleapis.com/ajax/libs/dojo/1.10.0/dojo/dojo.js"></script>

    <body class="claro">
      <select multiple="true" dropdown="true" name="multiselect" data-dojo-type="dojox/form/CheckedMultiSelect">
        <option value="TN">Tennessee</option>
        <option value="VA">Virginia</option>
        <option value="WA">Washington</option>
        <option value="FL">Florida</option>
        <option value="CA">California</option>
        <option value="TN1">Tennessee</option>
        <option value="VA1">Virginia</option>
        <option value="WA1">Washington</option>
        <option value="FL1">Florida</option>
        <option value="CA1">California</option>
        <option value="TN1">Tennessee</option>
        <option value="TN2">Tennessee</option>
        <option value="VA2">Virginia</option>
        <option value="WA2">Washington</option>
        <option value="FL2">Florida</option>
        <option value="CA2">California</option>
        <option value="TN2">Tennessee</option>
        <option value="TN3">Tennessee</option>
        <option value="VA3">Virginia</option>
        <option value="WA3">Washington</option>
        <option value="FL3">Florida</option>
        <option value="CA3">California</option>
        <option value="TN3">Tennessee</option>
      </select>
    </body>

<!-- end snippet -->