Unfortunately you cannot determine the type of the Account a user has (i.e. Personal, Premier or Business) however, you can check to see if the member is "verified". Here's one method.
1. First you need somebody's email address...
( Let's use potato @ potato.com as an example. )
2. Go to PayPal, and log in
3. Copy and paste this url:
https://www.paypal.com/verified/pal=username @ emailhost.com
4. Replace "username @ emailhost.com" with the person's email address
( In the example, it'd be https://www.paypal.com/verified/pal=potato @ potato.com )
5. The resulting page will show whether or not that email is linked to a verified PayPal account.
( It will show potato @ potato.com is NOT Verified in bold, red letters. )
Note, for the sake of posting, spaces were added to both the email addresses and URLs.
Make sure you remove the spaces when testing with your browser.
Additional notes per PayPal's info:
What it Means to be Verified
To become Verified, a PayPal member in the United States must provide us with proof that he or she has opened an account at a bank or other financial institution. Because these institutions are required by law to screen account holders, PayPal's verification process increases security when you pay parties you do not know. Please note that PayPal's verification system does not constitute an endorsement of a member, nor a guarantee of a member's business practices. You should always consider other indicators when evaluating members, including length of PayPal membership and reputation scores (on eBay or other auction sites, if applicable).
