My first piece of advice is to think carefully before bringing the police into your dispute unless there has been any kind of significant violence involved. Admitting to physical contact no matter how innocent or minor will force the police in many states to arrest that person. Often married couples who have different languages, cultures and customs misunderstand one another which can lead to disagreements and arguments. Make an effort to resolve disputes without involving those outside your family and community unless serious violence has occurred or there is a real possibility it will occur.
It may be possible, in certain situations, to avoid losing your Green Card and being Deported if the person gets an Immigration Attorney involved right from the beginning. Court cases and charges can sometimes be modified to avoid the immigration effect on your green card or status in the United States. If you were convicted, you will need all the court and other related documents. In many case, if the touching is minor, with no injury resulting the loss on a person’s Green Card can be avoided.
Beware that this can come up often years later when one returns to the U.S. after a trip out of the country or applying for Naturalization. One of the biggest mistakes people make is thinking that because they have not heard anything from U.S. Immigration for years since their arrest and or conviction that they are not in danger of losing their Green Card or other Status in the United States. There are many situations where the government has just not noticed you but each time you go outside the country or apply for some immigration benefit you are at risk of bringing that arrest or conviction to the governments attention and they will take action once it has been noticed.
Please contact a licensed Immigration attorney before you act on your specific situation. Immigration Laws and Federal Regulations are constantly changing and the general information provided can change over time.