The information that is available via MDT or MDC varies between deptartments depending on what software package they use and what options they utilize.
Pretty much standard would be access to DMV, NCIC, and other warrant lookups. Most will have a messaging feature also so units can type between each other.
What I think you are refering to is CAD access. Some deptartments have the ability to run CAD sessions on their MDC so that the officer can fill in all appropriate information and have information such as times and log/report numbers available without asking the dispatcher over the air. They can also see a summary of all on going calls and available units. There are software packages that integrate the CAD and MDC software so that when a unit is dispatched it is automatically sent all the information over their MDC.
Access to any of these services would be password protected and would obviously be illegal to access. It would also require specific hardware and software. This information can be sent over a trunk system or convention system.
There are departments out there that offer an online CAD that just shows the summary screen displaying type of call, location, and times. I know Warren County, NJ has this type of thing available online.
Mike