On father demise you and your sister have equal share in property 

2) your sister has to execute gift deed or relinquishment deed for her share in property 

3) it should be duly stamped and registered 

4) if it is a flat approach society to transfer flat in your name on basis of gift deed or relinquishment deed executed by sister 

Since the property is situated in U.S.A., the transfer of property applicable to USA will apply and our answer based on Indian Laws will not have any legal validity in the instant case.

Texas does not impose a state inheritance or estate tax. Most of its laws surrounding inheritance are straightforward.

However, if your father is reported to have died intestate, i.e., without a will, the distribution of his assets will be left up to the state’s intestate succession process. 

Estates with no will or a will that has not been probated by the Texas courts within four years of the deceased’s death can be inherited via the use of an affidavit of heirship. Someone with knowledge of the decedent and his or her family, as well as a public notary, must sign the document to transfer the estate to the decedent’s heirs at law

Biological children of the decedent and his or her spouse hold some of the strongest inheritance rights to an intestate will’s property.

In turn, an intestate will, because it has little to no pre-specified direction, is inherited by some combination of the deceased’s spouse, children and/or relatives. To differentiate between your belongings and whom they should go to, Texas divides them into community property and separate property.

The properties left behind by your deceased father, who is reported to have died intestate shall devolve  on the successors in interest/ surviving  legal heirs as per the law of inheritance of the law applicable to law where the property is situated. 

You may ask/request your sister to express no objection to your inheritance of the property by compensating her with the consideration amount equal to the value of her share in the property.

The laws prevailing in Texas i.e., the law of Inheritance applicable to Texas shall be applicable to the property situated in Texas

The laws prevailing in Texas i.e., the law of Inheritance applicable to Texas shall be applicable to the property situated in Texas

You may better spend some money on the local attorney in Texas and get the advice after consulting the attorney practicing law in Texas state instead of sending this question across globe to the advocates who are not aware of the local laws prevailing in Texas and don't be misguided by .false or misleading opinions rendered by other lawyers.  

If he has will you can do it through will otherwise need to go for succession certificate. If you have mother and other heirs you can go for family settlement deed too

As per Indian law, when a person dies intestate, i.e., without  making a will or any document with regards to his property, then  his assets will be distributed among his legal heirs through intestate succession process. The property is in Texas, so the law in Texas is also applicable.Dying without a valid will leave the distribution of assets up to the intestate succession process of the state of Texas.  children will receive an "intestate share" in the property.Biological children of the decedent and his or her spouse hold some of the strongest inheritance rights to an intestate will’s property. 

As per property law in Texas, the property divided in two types 

1. Community property - is a property acquired after marriage 

2. separate property - is the property  acquired before marriage 

if a person leaves the property with spouse and children, then  Texas deals with separate property differently. Spouse will inherit half of the community property unless the husband leaves descendants – children, grandchildren, or great grandchildren. If have separate property spouse will inherit all or a portion of it. The size of your spouse's share of your separate property depends on whether or not you have living parents, children, or siblings. If you do, they and your spouse will share your separate property.The state divides separate personal property between spouse and your children, with two thirds afforded to all the children and the leftover one third going to the spouse. 

The surviving spouse automatically receives all community property.

- As per law, after the demise of your father , his property would be devolved upon all the legal heirs equally ,i.e. you, sister and even the legal heirs of siblings who has died. 

- However, as the property is based in US ,then Indian court is not having jurisdiction for the same. 

Dear Client,

The share in property will be divided according to the will left by your father. In case he dies intestate the court will determine the share. Also, the laws in each state in USA might differ to is better to consult a lawyer practicing in that state. 

1. The property ihs been equally inherited by you, your sister and all other legal heirs of your deceased father.

2. The property can stand solely in  your name provided all the legal heirs of your deceased father releases their shares on the same in your favour by registering  Deed of Conveyance.

It will be prudent on your part to consult the Lawyers dealing with Real Estate in Texas to find out if there is any specific rule/rider in dealing with the said matter.

You should contact a local lawyer in Texas for drafting gift deed or relinquishment deed