The “state” in Kaduna State should be capitalised because the individual words that make up a proper compound ought to be. Kaduna State, not Kaduna state. But since this is not, strictly speaking, a grammar problem, an individual’s preference is to be respected as long as consistency is maintained. Now, let’s look at the matter in depth.
The basic rule is that proper names are capitalised, that is, written with the initial letter in capital—Ghana, Oguta, Idongesit, Zinox, Tallahassee, Oya. When the name is a compound, that is, has two or more parts, the individual words are capitalised—Oguta Lake, Michael Okosodo, Obudu Ranch, River Thames, Real Madrid, Oil Rivers, Fouta Djallon, Aswan High Dam. This is called a proper compound or, if you prefer, proper compound noun. Kaduna State is a proper compound. This simply means the two words make up a proper name and the two words are not two names but one.
It would be correct to write Kaduna state if “state” were a mere description; that is, if people normally say Kaduna when referring to Kaduna State and the “state” is not a part of the name. This is not the case. The “state” is a part of the complete name such that when it is removed, the name is not complete, although people sometimes do so in informal situations if the meaning is provided by context. Recall that Kaduna can refer to a river, a state or a city. River Kaduna. Kaduna State. Kaduna city or, simply, Kaduna. The first two are compounds but the third is not. When you want to refer to the city you simply say Kaduna. Adding city is merely descriptive so it is not capitalised. That is why we capitalise Benin City or Salt Lake City but not Calabar city or Lagos metropolis. It is for the same reason that we capitalise Igun Street, Herbert Macaulay Way, Oguta Lake and the others.
The non-capitalisation of the “state” in Kaduna State by elements of the local and foreign press is likely a practice picked up from the American system. But this approach is misguided. In the United States, unlike Nigeria, the names of the states do not include the “state”. When you say California, that means the state of California so the name is quite complete. Adding “state” is merely descriptive, usually for contextual or comparison purposes; therefore, it is not capitalised. This applies to similar constructs, such as Yola town, Lagos city, Fouta Djallon highlands, Kaiping watchtowers.
I am not laying down any rules here. I am merely describing the situation as it is. While Kaduna State is more accurate that Kaduna state, I will not be so cheeky to tell someone he is wrong to write Kaduna state, especially if he maintains his consistency. Maybe he even writes Igun street, Herbert Macaulay way and river Niger!