While the public sector doesn’t necessarily generate revenue, at the most basic level and similar to the private sector, IT allows you to either cut costs, or serve more constituents. It is rare even in the private sector that IT can be tied to direct revenue generation, so I see the public and private sectors as more alike than different in terms of IT metrics.
An easy metric for any industry is transactional costs. For example, if you are the DMV it should be a relatively easy exercise to determine the time and cost to serve a customer on a variety of transactions from providing a new license, to registering a vehicle. New IT systems and processes should reduce that transactional cost, and then calculating your ROI is as simple as multiplying the per transaction savings by how many transactions of that type occur. Care should be taken to ensure you also monitor outside variables so you’re not “passing the buck.” If I can cut 3 minutes off my process by giving you 30 minutes of work, then the net savings are obviously negative.