I can't seem to get the dependent dropdown to clear its value, but this does show the dependent search having a cleared value from the dependent dropdown until a new value is selected: 
  <form>
  <label>States</label>
  <search id="states">
    <query>| makeresults | eval state="Alabama,Alaska,Arizona,Arkansas,California,Colorado,Connecticut,Delaware,Florida,Georgia,Hawaii,Idaho,Illinois,Indiana,Iowa,Kansas,Kentucky,Louisiana,Maine,Maryland,Massachusetts,Michigan,Minnesota,Mississippi,Missouri,Montana,Nebraska,Nevada,NewHampshire,NewJersey,NewMexico,NewYork,NorthCarolina,NorthDakota,Ohio,Oklahoma,Oregon,Pennsylvania,RhodeIsland,SouthCarolina,SouthDakota,Tennessee,Texas,Utah,Vermont,Virginia,Washington,WestVirginia,Wisconsin,Wyoming" | makemv delim="," state | table state | mvexpand state</query>
  </search>
  <fieldset submitButton="false">
    <input type="dropdown" token="letter" searchWhenChanged="true">
      <label>Letter</label>
      <fieldForLabel>letter</fieldForLabel>
      <fieldForValue>letter</fieldForValue>
      <search base="states">
        <query>
          <![CDATA[rex field=state "^(?<letter>.)" | stats count BY letter]]>
        </query>
      </search>
      <change>
        <unset token="state" />
      </change>
    </input>
    <input type="dropdown" token="state" searchWhenChanged="true">
      <label>State</label>
      <fieldForLabel>state</fieldForLabel>
      <fieldForValue>state</fieldForValue>
      <search base="states">
        <query>
          <![CDATA[rex field=state "^(?<letter>.)" | search letter=$letter$]]>
        </query>
      </search>
    </input>
  </fieldset>
  <row>
    <panel>
      <title>You picked</title>
      <single>
        <search base="states">
          <query>search state=$state$ | table state</query>
        </search>
        <option name="drilldown">none</option>
      </single>
    </panel>
  </row>
</form>
  
						
					
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