JSFiddle - React, Tailwind, and code Playground

HTML

<div>
  <img src="http://iconizer.net/files/The_Centigrade_MedicalSeries/orig/Select.png" alt="select">
  <select>
    <option value="1" selected>test 1</option>
    <option value="2">test 2</option>
    <option value="3">test 3</option>
  </select>
</div>

CSS

* {
  margin: 0;
  padding: 0;
}

div {
  position: relative;
  width: 200px;
  background: white;
  margin: 20px;
}

img {
  position: absolute;
  right: 0;
  z-index: 1;
}

select {
  position: relative;
  width: 100%;
  height: 30px;
  background: transparent;
  border: 1px solid #CCC;
  -webkit-appearance: none;
  z-index: 2;
}