You would need to add your drop down to contact_form.tpl :
<select name="recipient">
<option value="staffmember@website.com">Staff Member</option>
<select>
And in the php you would need to find the part where it mentions:
Util::SendEmail(ADMIN_EMAIL, $subject, $message);
and change to:
Util::SendEmail($this->post->recipient, $subject, $message);
where recipient is the name of your dropdown.
I think