I could not find any information on how to use an actual CSS class in a cflayout or cflayoutarea attribute like so:
<style>
.layoutStyle{..}
</style>
<cflayout class="layoutStyle">...</cflayout>
I guess it's simply not possible, but I have a work around, sort of. Not really using a css file but basically declaring the class name as a variable equal to the style attributes desired. Then use that variable in the layout style attribute:
<cfset layoutStyle = "width:800; text-align:left;">
<cflayout style=#layoutStyle#>...</cflayout>
An alternative is to set the styles in ini or txt files and use them externally, which is the point of css to begin with, external style sheets.
I have enough information regarding cascading style sheet and its advance features yet you have posts does help.