If you use the "Married Filing Joint" status for the DC return, DC will factor in all of your income to determine the DC part-year tax on your wife's income. DC would pretend that both of your income were taxable in DC, and then prorate the tax to the percentage of income actually earned in DC. DC doesn't actually tax your income, but it does use your income to determine tax.
However, DC will also allow you to use the status of Married Filing Separately to compute tax on just your wife's income, and you are allowed to use the method that results in lower tax.
To file a DC separate return when you are preparing a joint Federal return, please see this FAQ: https://ttlc.intuit.com/replies/3301995