Can I get penalized for not filing state taxes even if I owe nothing?

If your income is more than the filing requirement, then you must file the tax return. If you don't file and don't owe tax, you will normally not have to pay any interest and penalty, but if you owe any amount, then the amount due will keep on multiplying.
This can also happen if state makes some changes in your tax return.
File soon.

I am no expert and I don't think you provided enough information but I would say there probably are instances where you could be required to file even if you don't owe.

Tax booklets usually tell you on the first few pages:

"Who must file"
If you don't have to file based on a review of that section, you should be OK

If the state requires a tax return be filed and you do NOT file, they eventually will analyze your tax data (they receive this data in the form of W-2s, 1099s, etc.) and prepare a draft return using the worst-case scenario (normally Married Filing Separately).

If you owe money on that worst-case scenario, then they try to get you to file a tax return to collect the taxes due.

If you do NOT owe money, then they do not bother, because they have already been paid. Your failure to file just denies you the tax refund to which you are entitled.

Case in point: I had a client in Georgia who failed to file the GA state tax return for FIFTEEN years. Georgia did not bother them about it until the 16th year, when their early distribution from an 401K caused them to OWE Georgia a small sum of money.

Then (and only then) did Georgia send them a notice demanding that they file that year's (2004) tax return, plus ALL of the previous years' returns. The client came to me to negotiate the issue, and when I contacted the Georgia Department of Revenue, I negotiated in person for about three hours, during which time I pointed out that the Georgia tax forms were NOT AVAILABLE prior to 1996. When the GA DoR found that THEY did not have blank forms available prior to 1996, they relented and allowed me to submit ONLY returns for 1996 onward.

Unfortunately, the client could NOT recover refunds prior to 2002, and ended up forfeiting about $8,000 worth of tax refunds.

Moral of the story: Make sure you file even if not legally required to IF you have a refund coming. You have THREE years to claim your refund. If you fail to do so, you LOSE the money!