@jonhai - please clarify,

Where you work is a question of the physical location - not a virtual location.

So when you state you will work 'in Maryland" - please confirm you are traveling from Indiana to Maryland each week for this position.

if you are working for a Maryland based company and physically sitting at a desk in Indiana, you are not 'working in Maryland.  is that what you mean by "remote"? 

also, I assume this is a W-2 position and you are not a contractor. 

@NCperson Thank you for your quick. response. I updated my post. Yes. I will work remotely. My work only needs a laptop. I am a contractor. 

Per OP, 

 I am a contractor.

@jonhai if you are a contractor, your "employer" is not going to withhold ANY taxes, whether that be federal, state, social security or medicare taxes.  Federal and State taxes will be your responsibiltiy to make estimated payments each quarter (and the federal includes the social security and medicare taxes) 

at the end of the year this 'employer' will issue you a 1099-NEC for your income taxes.  

@jonhai --

I strongly suggest that you clarify with your employer as to whether or not they will be withholding federal taxes from your pay.

Ideally they would withhold both federal and Indiana taxes for you (assuming you're never going to physically work in MD).  If there's going to be no withholding at all, then you will need to make both federal and Indiana quarterly estimated payments as stated by @NCperson.

If they are going to withhold federal - but not Indiana - taxes, then you'll need to make estimated tax payments only to Indiana. 

 https://www.in.gov/dor/individual-income-taxes/payments-and-billing/estimated-tax/

@jonhai - also, understand that when you are a contractor and not a w-2 employee, the requirements of whomever is paying you are quite different.

when you are a W-2 employee, the employer has obligations to withhold federal, state, social security and medicare taxes based on federal and state laws.

when you are a contractor, whomever is paying you do not have those obligations, so it is up to you to pay the appropriate taxes

Thank you so much for your input. I sincerely appreciate it. In my case, do I need to pay Maryland state tax and the special nonresidents tax rate? I was reading the link below and got confused. Thank you again! 

https://www.marylandtaxes.gov/individual/income/tax-info/index.php

"Nonresidents are subject to a special tax rate of 2.25%, in addition to the state income tax rate."

@jonhai - you are not a non-resident of Maryland..

You work and live in Indiana. Period.

A non-resident would be someone who PHYSICALLY works in Maryland (you don't) and lives in another state.  Think of someone who lives in West Virginia and commutes into Maryland for their job - that would be a non-resident. 

@jonhai --

I apologize for being a nitpicker, but as a resident of Indiana you definitely are a non-resident of Maryland.

The issue is that Maryland taxes non-residents only on Maryland-source income.

Work income is "sourced" where the work is actually (physically) performed.  (There are a few exceptions but they are not relevant to your case.)

Since your work is actually performed in Indiana, your income from that work is Indiana-source income, and therefore not subject to Maryland state income tax.

Think of this example:  Coca-Cola is headquartered in Atlanta, Georgia.  But that doesn't mean that all Coca-Cola employees across the country pay Georgia state income tax.  The only Coca-Cola employees who pay Georgia income tax are those who live in or physically work in Georgia. 

Thank you so much for your help. I really appreciate it.