Here are some directions: With Rafflecopter, you can create an entry option that asks your entrants to leave a blog comment, which will direct the entrant to leave a comment on your blog. You can also have your entrants leave a comment or a bit of information inside the widget by using the 'invent your own' entry option. Here's a blog post that outlines this process.
Rafflecopter doesn't directly tie in with blog commenting software. If you're trying to verify your winner who left a blog comment, you should be able to match up their name, email address, IP address, or timestamp. If you have it set up for entrants to leave their comments inside the widget, these comments will be hidden from public view, but can be accessed by you on your giveaway's entries page.