I would suspect the state deduction would be adjusted by the personal/business use percentage. e.g., if you deduct 10% of expenses as home office on federal, you'd get 90% of the state amount. BUT, if it's up to $3,000 and your 90% comes out to more than $3,000, you might still get $3,000? This is why it's important to know the state, but this is the kind of stuff to look for.

Also, be warned that by claiming a home office you open up a different can of worms many people ignore. A) If your landlord requires tax returns to prove income but is super strict in the lease about no business use of the apartment. B) If the state/local government sees your home office deduction and you have to pay some sort of franchise tax or get some sort of permit. For A, most leases explicitly allow telecommute computer-only type stuff now, but for B, I've seen the locals fuck people over even when it's something like a remote developer who's 1099 for a single company.