i just started using google's webmaster tools for my website. and i don't see if they provide information as to whether or not backlinks are dofollow or nofollow.
Google webmaster tool has no option to show you the DoFollow or NoFollow backlink. You have to install the QuirkSearch Status Plug In from Mozila Firefox.
There is a firefox extension "nodofollow" that differentiate links that are nofollow & dofollow, through colors of links.
I'm using Search Status Plugin for firefox for identifying nofollow links. It's a good tool to have if you're in SEO stuff.
Google webmaster tools does show some nofollow backlinks in your account, however it does not separate dofollow and nofollow in your account. What the criteria is for showing some in wmt is I have no idea, but some are definitely nofollow.
If you want to know whether the incoming links are do follow or nofollow you will have to use a famous web tool called Backlinkatch
To check whether or not the page is dofollow or nofollow, you can check out the page info/page source. Then you search nofollow within the codings. If there is nofollow words detacted, meaning the site is nofollow.
Yes its right that there is no option in web master tool about identify no-follow or do-follow links, for this purpose you should go for watch backlink (dot) com
With the help of Google webmaster tool you can find out the number of indexed pages of your site which includes both dofollow and nofollow link.
There are various add-ons that shows the no-follow attribute of the link.. Just google it out and you will get the best of them.
I most like Nodofollow add-on for Firefox,but it doesn't work in firefox 4,swoosty SEO also can do this.