The search form is found within your theme's searchform.php
file. If your theme does not have one, creating one will override the WordPress default. You might do something like:
<li id="search">
<label for="s">Search:</label>
<form id="searchform" method="get" action="/index.php">
<div>
<input type="text" name="s" id="s" size="15" />
<select name="searchcat">
<option value="0">Search Posts & Pages<option>
<option value="1">Search WooCommerce Products</option>
<option value="2">Search Custom Post Type</option>
</select>
<input type="submit" value="Search" />
</div>
</form>
</li>
The search results are found in the your theme's search.php
file. Again, if your theme does not have one, you can create one to override the default functionality.
Then, based on what it selected from the pulldown, you can create different queries to retrieve the required results.