Can I skip Immigration Court date if I just want to leave the U.S. on my own?
It's better to show up and save yourself from an order of deportation on your record by requesting "voluntary departure."
I was stopped for speeding and the police officer realized I did not have authorization to live in the United States. They called immigration and I now have to go to a hearing in Immigration Court. I just want to leave and go back to my home country. Can I do that?
You must make every effort to attend your hearing in immigration court on the date you are scheduled to appear. If you do not appear for your immigration court hearing, you will be ordered removed by the immigration judge.
One consequence of an order of removal on your file is that you will not be able to reenter the United States for up to 20 years, or even permanently, depending on the facts of your case. So, for example, if you were to marry a U.S. citizen, win the diversity visa lottery, or be offered a job by a U.S. company willing to sponsor you for a visa, your prior removal order would block these immigration possibilities. If you are ordered removed and attempt to reenter the United States before you are legally able to do so, you can be charged with a federal crime.
You may, instead, choose to appear for your hearing and request what’s called “voluntary departure.” To determine whether or not you are eligible for voluntary departure see Nolo's article, "Voluntary Departure: Who Is Eligible?" The main benefit of requesting voluntary departure is that you will have between 60 and 120 days to leave the United States and no removal order will be put on your immigration record.
In addition, you may also be able to reenter the United States (legally) sooner. To determine when you might be eligible to re-enter the United States, please see "Consequences of Unlawful Presence in the U.S. -- Three- and Ten-Year Time Bars."