Tailwind CSS is not exactly providing solutions for form elements like Select-tags and co. that work on all major browsers.
If you apply those from Tailwind CSS, you may either add your own elements (e.g. arrows) for a Select tag, inputs, and co. or work with CSS. You can also look on how developers solved these issues with examples from Tailwind Components.
Tailwind CSS Forms was made to make this possible and it works with Tailwind CSS 2 while Tailwind CSS Custom Form is deprecated.