Can I file my state taxes separately on TurboTax if I’ve lived in two different states for 2020?

You have to file part year returns in both state.

Your W-2 forms should show which taxes and income belong to which state.

For your state returns - you must do a return for each state.  You need to report the income that was correct for each state.  Simple example - if you earned a total income of $50,000 for the year and $25,000 happened in MD and $25,000 happened in IN - then you file a FEDERAL return for the total of $50,000 but you file TWO state tax returns - one for each state - claiming $25,000 for each state.

Again, that is a simplified example - but you would only be paying taxes to the state based on what you earned in that state, so you need to separate the income according to location.

Turbo Tax should be able to handle two states.  You may be filling in something incorrectly.  

You have to do them separately, you cannot file two states in one return.

If you're getting different results then you're making a mistake on one of the calculations.

Turbo Tax can handle and accurately compute both of your partial year state returns IF you put the data in correctly.

Before you just run off and file the returns separately, figure out where you're making the mistake. The returns should match whether you file them all at once or one at a time.

You've probably not done the state allocations properly.  You should only be taxed in Maryland for what you earned while a resident there. You need part year resident returns for both states.  You should get a credit on your Indiana return for some or all of the taxes you paid to Maryland.  As with any computer program, the inputs have to be correct to get the right answers.  You might want to consider taking your taxes to a private preparer in your area.  You can find a list of ones near you on the IRS website.

No, you can not file them separably.

None of the online tax programs do very well with returns with multiple states.  Tax software and websites can only be as good as the person inputting the data.  How well do you understand how multi-state issues are handled on the tax return?