For example, I want a CSS selector for all div
elements which have a CSS overflow:auto;
property. Is it possible to have a selector of that kind?
No. There's no way to do this with css. You need to use scripting language.
But if you have defined style in your html like the following then this would be possible like:
div[style="overflow:auto;"]{
background-color: #f00;
}
<div style="overflow:auto;">overflow is auto</div>