How to define `autocomplete="off"` as a CSS style?

Using CSS you cannot achieve it. You can use client side script for example using Jquery

$('input').attr('autocomplete','off');

If you are not using Jquery or scripting language then you have to stick to HTML only.

As TeT Psy said you can apply it in form tag like

<form id="Form" runat="server" autocomplete="off">

you can disable all the autocompletes using form

<form id="Form1" runat="server" autocomplete="off">

You can use autocomplete="off" attribute on form tag. Like this:

<form id='test' autocomplete="off">
  <input ...
  <input .. 
   ...
 </form>

No you can't do this using css, but there are 2 other ways to do it:

1- you can apply it for the form

<form autocomplete="off" >
  <input type="text" name="name">
  <input type="text" name="mail">
</form>

2- you can handle it using js

var eles = document.getElementsByTagName('input');
for(i=0; i<eles.length; i++){
    eles[i].setAttribute("autocomplete", "off");

}

https://jsfiddle.net/ng1mb77m/1/

You can set it on form element if you wants to set autocomplete: off for all input elements of form. And if wants to make it on for some selected input you can apply autocomplete: on on that input.

.form {
  padding: 30px 0;
  width: 300px;
  margin: 0 auto;
}

<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css" rel="stylesheet"/>
<form action="#" class="form" autocomplete="on">
  <div class="form-group">
    First name:<input type="text" class="form-control" name="fname">
  </div>
  <div class="form-group">
    Last name:<input type="text" class="form-control" name="lname" autocomplete="off">
  </div>
  <div class="form-group">
    E-mail: <input type="email" class="form-control" name="email">
  </div>
  <input type="submit">
</form>