Short answer, the same bankruptcy rules apply to state income taxes as do federal income taxes.
As to your specific situation, you would need a retroactive tax discharge analysis to figure out where you stand.
I happen to offer such a service to both attorneys and non-attorneys. See the link below.
It is not possible to answer your question without the following information: for what tax year are the taxes; what type of taxes are they (income, withholding, excise, sales, etc...); when did you file a return; was a substitute for return prepared and filed for you by the taxing authority; what was the date of your bankruptcy filing? If you can determine the relevant data, then you can read section 507(a)(8) and 726 of the Code to determine dischargeability. You will not get that level of detail answered in this forum for free.
Posting questions anonymously and receiving general answers do not substitute for consulting with an attorney licensed to practice in the jurisdiction in which you live. Answers posted here by Kevin C Gleason are only intended for general education of the public on legal matters. Please consult a qualified professional before deciding what to do about your situation.
Discharging taxes is a more complicated analysis as my colleague pointed out. You would really need to consult with a knowledgeable bankruptcy attorney to do that properly. As a general matter, if you did not timely file your returns and the taxing authority filed a substitute return, it will not be dischargeable. Again, you really need to seek counsel on this. Good luck.
This answer is for informational purposes only and is not intended as legal advice or to create an attorney-client relationship.