It doesn't hard for adding this widget to your blogger and you need to spend only few minutes to do this. So now let's start with me step by step
Demo: How to add drop down label widget to blogger
1. Log in to blogger account and Go to Design >> Edit HTML
2. Right click on edit html box
3. Using Ctrl+F to open search box and then searching for code below
<b:widget id='Label1' locked='false' title='Labels' type='Label'/>
4. Now replace above line (where you found) with below code.
<b:widget id='Label1' locked='false' title='Categories' type='Label'>
<b:includable id='main'>
<b:if cond='data:title'>
<h2><data:title/></h2>
</b:if>
<div class='widget-content'>
<select style='width:100%' onchange='location=this.options[this.selectedIndex].value;'>
<option>Choose a Category</option>
<b:loop values='data:labels' var='label'>
<option expr:value='data:label.url'><data:label.name/>
(<data:label.count/>)
</option>
</b:loop> </select> <b:include name='quickedit'/> </div> </b:includable>
</b:widget>
Note : *You can change the wdth of drop-down by chaning 100%
*You can change Choose a Category as your like, if you want.
*If you want to hide the post counter so delete this code. (<data:label.count/>)
5. Save your Template you are done.

