Not specifically: however, when you create a webmail account with providers such as Yahoo!, the OpenID system enables you to use this account data to sign in to numerous other websites: such as Youtube, blogs, newspaper websites etc.
Due to the massive amount of websites, it can become a laborious task to create an individual account for each of them: to store the account data and remember it etc. The purpose of OpenID is to simplify this process so you can use the account details of one website on hundreds of other websites. The account you create does not have to be a webmail account: it could be a Linklin or Twitter account for example. So, in that sense, there is no specific connection between OpenID and webmail.
You will need to perform a few simple tasks to "tie" your webmail account to a OpenID identifier. With Yahoo! for example, you need to: sign in with your account; select the account info page; then find the links which says Manage/Create your OpenID; follow the instructions on that page and you should have your OpenID up and running.
The OpenID identifier you select can be different the webmail account name you use; in fact, most webmail services suggest you pick a different OpenID identifier than what you use as your webmail username. However, you can still login to OpenID with the username you use on your webmail account.