If I take the standard education on my Federal return, must I also use it on my Maryland return, or can I take itemized deductions on the State return?

Yes, you must. Here is what the Comptroller of Maryland states:

Under current Maryland law, if you take the standard deduction the federal level, you cannot itemize at the Maryland level. You may take the federal standard deduction, while this may reduce your federal tax liability, it may result in an increase to your Maryland income tax liability. The Comptroller’s Office encourages you to run your income tax returns under both deduction methods and to compare the results of taking the standard deduction versus itemizing your deductions, to see which method causes the lowest overall tax liability.

For further information, here is the link from Maryland:

https://taxes.marylandtaxes.gov/Individual_Taxes/General_Information/What_s_New_for_the_Tax_Filing_S...