Unfortunately, no, you can only include the state tax paid. It is true that some states do calculate both state and local taxes on the state return, but, as you mention, they still consider them as separate "buckets" so to speak. There are some states that do give credit for local taxes paid to other states because of this, but California is not one of them.
TurboTax will actually do this for you if you first prepare the Maryland return. It will calculate the correct amount and carry it over to your California return to get credit for the taxes paid to another state (in this case Maryland). Here is an FAQ with instructions on how to do this: : https://ttlc.intuit.com/replies/3302052
Also, you may qualify for certain deduction on your Federal return if you were travelling to Maryland to work. Here is an IRS Publication link that talks about what you may be able to deduct: Publication 463. (If you have questions, feel free to comment and I'll be happy to assist).
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