You can check on your state's (lack of) pension funding on this WSJ table. The worst offenders are, in order, IL, KY, CT, AK, KS.
I would avoid owning any muni's from these states unless you are going to read all the fine print about the priorities of funding, revenues, etc, and even for the bold, stick to shorter dated bonds (maybe 5-10 years, definitely not 30 years). Some of these states are where Puerto Rico was 5-10 years ago, and like most defacto bankruptcies, it happens very slowly and then very quickly. As soon as there's a crisis of confidence in a state's ability to repay its bonds, no interest rate is high enough and they will have a hard time rolling over their debt to finance their unsustainable budgets (of course they have unsustainable budgets or they wouldn't be in this mess in the first place). You won't want to be long that state's pension or muni's when that happens.
Interest rates are moving higher, and that will also shift up their debt interest costs and future issuance rates. Like PR or IL have already seen, a state can raise money primarily by taxing locals and if their tax rates get too high people will just leave. Already many of the high tax rate states are seeing net outflows of $B of taxable AGI annually to FL and similar places in recent years, and the kinds of steps to address the pension gaps by socializing those generous past promises onto the average local taxpayer are the kinds of things that accelerate this exodus. The recent tax reform has mostly removed the federal subsidy for high state taxes, so high earners will feel the full impact of any marginal tax increases. While not everyone can pick up and move to Florida (or Texas or Nevada...), the progressive tax code hits the wealthy disproportionately and they are more able to move their job or their business elsewhere if the economic environment changes too much for the worse.
It's not a pretty picture. You're playing a game of chicken as a muni owner in these fiscally mismanaged states, betting you'll get out (or get a bailout) before the day of reckoning arrives. That's not a game I would be playing, but you pay your money and you take your chances.