Yes, You can directly connect the database with your web services. But it is not proper way to do.
If you will connect directly to your database, It may be increase your code quantity and decrease the performance. Also the quality of the code will be decreased.
You should use BAL to separate the business logic and your code will be neat and clean.
here are some good examples of usually what we are using. Consuming Webservice using JQuery ASP.NET Application
Web Services using JQuery AJAX
Update
Although if you wanted to connect webservices directly to the database, here is the link : Call database from webservice