Are you talking about a client-side API? There are a couple of ways to go, depending on which features you want. You may be able to get away with using an existing C# POP3 or IMAP library. I don't have a lot of experience with C# mail libraries, but a quick Google search returned this one, among others:
http://www.codeproject.com/csharp/IMAPLibrary.asp
If you need access to Zimbra-specific features, such as conversations, you'll have to write a C# library that wraps our SOAP messages. Our SOAP API is documented in ZimbraServer/docs/soap.txt and soapadmin.txt.