I've lived in California for 1yr + rent/work there. I haven't had a time to change driver's license. It's registered at my dads address in MN. Do I need to file in MN?

Unless you had MN income other than wages (e.g. rental property?) or had MN tax withheld from your CA wages (unlikely),  you don't need to file a MN tax return.

Having a driver's license from a state does not make you a resident of that state.

What makes you a resident of a state (or country)? 

Generally, you're a resident of a state (or country) if you intend to either stay there permanently, or return there after a temporary absence. It's where home is – where you come back to after being away on vacation, business trip, overseas or out-of-state employment, or school. Many factors are considered, not the least of which are where you are registered to vote, own homestead property and are licensed to drive.

Residency rules vary from state to state. For example, if you spend more than a certain number of days in some states, you're considered a resident whether it makes sense to you or not. If you have any concerns, check with your State Department of Revenue for specific residency rules, especially as they apply to your particular situation.