Just in case anyone is looking for a way to create a search form that provides selectable drop-down list of their custom post types, here is what worked for me:
<form role="search" method="get" id="searchform" action="<?php echo home_url( '/' ); ?>">
<input type="text" name="s" id="s" value="Enter keywords ..." onfocus="if(this.value==this.defaultValue)this.value='';" onblur="if(this.value=='')this.value=this.defaultValue;"/><br />
<select name="post_type">
<option value="">Choose Category:</option>
<option value="">All Categories</option>
<option value="post_type_a">Post Type A</option>
<option value="post_type_b">Post Type B</option>
<option value="post_type_c">Post Type C</option>
</select><br />
<input type="submit" id="searchsubmit" value="Search Help" />
</form>
Obviously, replace post_type_a with your unique post type name and Post Type A with your post type label. Good luck!
Justin
https://www.cerebralideas.com