It is possible to configure the web ssl connector to use the Windows certificate keystore (access provided by the SunMSCAPI provider). However, the JSSESocketFactory checks for a keystore file. This check should likely be skipped when the connector is configured to use the Windows keystore.
Here is what the configuration looks like:
This results in an error like this:
13:54:01,821 ERROR [org.apache.coyote.http11] (MSC service thread 1-5) JBWEB003043: Error initializing endpoint: java.io.FileNotFoundException: C:\Users\imauser\.keystore (The system cannot find the file specified)
You can work around this issue by creating this keystore (C:\Users\imauser\.keystore).
More info on using the Windows keystores can be found here: