Q:

Why does the combined cap gains tax rate not equal state + federal rate?

I often see "combined" capital gains tax rate tables. In fact, it is rare to find tables that just have the rates by state. Usually, it is a combined table. For example:
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This table is a little unusual in that it has both combined and state rates together. The math does not seem to add up though. The top federal rate is 25% as you can see from the New Hampshire line item. However, for Connecticut, since the cap gains rate is 6.70%, shouldn't the combined rate be 25% + 6.70% = 31.70%? Instead, it says 29%. Why is this?

A:

See the sixth footnote on that page for the explanation.  That is referenced from the topline number (mentioned earlier in the piece) and has the identical number as the topline number from this table (28.6%), so I'm confident they're the same calculation.

The U.S. average is the combined federal, state and local rates on capital gains, taking into account Pease Limitation and state/federal deductibility of income taxes weighted by capital gains income in each state.

So you notice the 0% states all are at 25% (which is the federal rate), but the states with > 0% reduce the total by various factors, the largest of which is probably the deductibility of state taxes on your federal return.  
It's unclear if the author reduced the total by the marginal rate on total income (39.6%) or by the marginal rate on capital gains (25%).  The former is more likely, both because it's the more likely actual result (the deduction reduces total income tax paid, not just capital gains, and so as long as the taxpayer has some non-capital gains income, they will be saving 39.6% of the state tax), and because from my simple calculations using my own state that matches closely.
$10000 capital gains
IL tax: 3.8% = $380
Fed tax: 25% = $2500
Deduction of IL tax: 380*.396 = $150.48
Total tax paid, net: $2729.52 = 27.29%

That's identical before rounding to the 27.2% number in the table; it's possible it should be 27.3%, or it's possible there is some other factor at hand here.  I'm ignoring the Pease limitation, which the author said he took into account, and I'm treating it very simply (I have no idea if Illinois has any particular regulations related to state capital gains, or really anything else, here), but the fact that I still get a similar number suggests that this is likely what's happening.

