Yes, you can as long as both you take the same deduction.
From Alabama:
You have the option to either itemize your deductions or you may claim the optional Standard Deduction. You should compute your deduction both ways to determine the option that gives you the larger deduction.
If married and filing separate returns, both spouses must claim the same deduction unless the spouses have lived apart for the entire year, in which case each spouse may claim either deduction. However, neither spouse may claim a deduction for expenses paid by the other.
Alabama Instructions on page 8:
https://revenue.alabama.gov/wp-content/uploads/2017/08/16f40bk.pdf
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