Question Regarding Property Tax

If she gets all the income and pays all the expenses then only she should report the rental on her return. 

I bought a home in my name with my sister.

The way I understand the above, is that both you and your sister are on the loan. I assume that you are primary on the loan and your sister is the co-signer. So you are both equally obligated to pay the loan.

Her name is only on the Title

No mis-understanding there. Only your sister is listed on the real estate title/deed for the property.

but the mortgage is under my name.

I assume you mean that you are the "primary" borrower on the loan, with your sister as co-signer. If my assumption is correct, then the 1098-Mortgage Interest Statement will be issued to you at tax time.

when it comes to income tax time

Your sister will report everything on her tax return since she is the one using the property to produce income for her alone.  She will most likely be the one to claim the mortgage interest, property taxes and property insurance on her tax return too, as I assume she meets both of the basic criteria to claim it.

1) Must be obligated to pay it.

2) Must actually pay it.

So if the property title/deed is in her name only, then she is obligated to pay mortgage interest (assuming her name is on the loan), property taxes and property insurance.

If her name is not on the loan, then it looks like she may have what's called "vested interest" in the property which is supported by her name being on the property deed/title. That would be enough for #1 above since she is also receiving all of the income/gain from the investment property.

My above on this is extremely simplified and should be enough for  you to "get it". If not, there are other participants in this public forum that can explain it if necessary, much better than I can.