Assuming you're using simple xml, Edit your dashboard xml to add timerange elements in your dropdown search.
<input type="dropdown" token="dropdownToken" searchWhenChanged="true">
<label>Dropdown label</label>
<fieldForLabel>value</fieldForLabel>
<fieldForValue>value</fieldForValue>
<search>
<query>your dropdown search</query>
<earliest>$timerange.earliest$</earliest>
<latest>$timerange.latest$</latest>
</search>
</input>
What do you want to be in the dropdown list? How does the list change based on the time selector?