Here is a working example using a button for demonstration purposes only.
Style property with the attribute as a key we are looking for must be applied to it.
Markup:
<asp:Button ID="Button1" runat="server" Text="Button" Visible="false" style="display:block;" />
Code behind:
var styleProp = Button1.GetType().GetProperty("Style");
if (styleProp != null)
{
var styleCollection = styleProp.GetValue(Button1, null) as CssStyleCollection;
var value = styleCollection["display"];
}
You would have to replace the button with which ever control you have already.