JSFiddle - React, Tailwind, and code Playground

HTML

<div class="select">
    <select name="month">
        <option value="na">Month</option>
        <option value="1">January</option>
        <option value="2">February</option>
        <option value="3">March</option>
        <option value="4">April</option>
        <option value="5">May</option>
        <option value="6">June</option>
        <option value="7">July</option>
        <option value="8">August</option>
        <option value="9">September</option>
        <option value="10">October</option>
        <option value="11">November</option>
        <option value="12">December</option>
    </select>
</div>

CSS

.select {
    width: 100px;
    overflow: hidden;
}
.select select {
    width: 120px;
    -moz-appearance: none;
    -webkit-appearance: none;
    appearance: none;
    text-indent: 1px;
    text-overflow:'';
}