JSFiddle - React, Tailwind, and code Playground

HTML

<div class="common-dropdown-small-div">
<select class="common-dropdown-project-select">
<option>Choice</option>
<option>One</option>
<option>Two</option>
<option>Three</option>
</select>
</div>

CSS

.common-dropdown-small-div{
    border: 1px solid rgb(208, 208, 208);
    overflow: hidden; 
    width: 220px;     
}

.common-dropdown-project-select{
   width: 100% !important;
    background-image: url("http://upload.wikimedia.org/wikipedia/en/f/f1/Down_Arrow_Icon.png");
    background-position: 97% 60%, 0 0 ! important;    
     background-repeat: no-repeat;
    background-size: 25px 16px;
    border: none  ! important;    
    outline : medium none !important;
    display: inline-flex !important;
    height: 33px !important;
    vertical-align: top;
    -webkit-appearance: none;
}
select::-ms-expand {
   
}