Residency has different meanings depending on the context. Generally you can't have two "homes"
You can only have one primary residence for the purpose of a sale of a home.
Sale of your main home You may take the exclusion,
whether maximum or partial, only on the sale of a home
that is your principal residence, meaning your main home.
An individual has only one main home at a time. If you
own and live in just one home, then that property is your
main home. If you own or live in more than one home,
then you must apply a "facts and circumstances" test to
determine which property is your main home. While the
most important factor is where you spend the most time,
other factors are relevant as well. They are listed below.
The more of these factors that are that are true of a home, the
more likely that it is your main home.
https://www.irs.gov/pub/irs-pdf/p523.pdf
You can only have one tax home for deducting expenses.
Generally, your tax home is the entire city or general area where your main place of business or work is located, regardless of where you maintain your family home. For example, you live with your family in Chicago but work in Milwaukee where you stay in a hotel and eat in restaurants. You return to Chicago every weekend. You may not deduct any of your travel, meals or lodging in Milwaukee because that's your tax home. Your travel on weekends to your family home in Chicago isn't for your work, so these expenses are also not deductible. If you regularly work in more than one place, your tax home is the general area where your main place of business or work is located.
https://www.irs.gov/taxtopics/tc511
General State Requirments
https://ttlc.intuit.com/questions/1901036-what-is-my-state-residency-status
