Hi,
I just started working in Pennsylvania. However, I still own my house in Maryland (and the driver's license). The HR lady asked me whether I preferred to keep my Maryland address or change it to Pennsylvania (using the business address) for tax purposes. I want to make sure that I don't have to pay taxes in both states. Any suggestion what would be the best way to proceed.
Thank you,
Lagu

Which state has the lower state taxes, TN for example has no state income tax.

PA has the lower income tax but if you claim residency in PA they will probably try to hit you with some of the other Borough taxes, school taxes etc. Plus you will have to register vehicles, get vehicles inspected each year (MD has emissions testing tho), get driver's license changed. Then, MD will question PA tags at your home, etc, etc.
We move to PA because they don't tax our retirement and we like it in PA, but we haven't saved much because of the ridiculous property taxes, school taxes, borough taxes. If this is short time, you definitely don't want to claim that address in my opinion.

You MUST file PA income tax return. It does not matter which one is your tax home. Any income earned in PA, must be reported on PA tax return.
Also you may also have to file MD tax return, if it is your tax home.
Read Your U.S. Tax Return: Working or Living in Two or More states

You need to determine what your state of residence is, and that depends on which state you spend the most nights in. If you are commuting on a daily basis from MD to PA, then you are still an MD resident, and you file MD taxes as before. MD has a reciprocal agreement with PA so that you only pay MD taxes and do not need to file a PA tax return. In this case you should tell HR to withhold MD taxes - see:

Maryland Tax Credits - Income Tax Credits in Maryland

This assumes you are still a MD resident. But if you are now renting an apartment in PA or own a second home there, and are sleeping overnight in PA more than you do in MD, then you are now a PA resident. The fact that you still own a home in MD and still have an MD driver's license is not relevant. In this case you would pay only PA taxes on your wages - which as stated earlier are generally lower than MD taxes, and so that would be to your advantage.