法律是这么规定的。你收到的绿卡或者welcome notice

（具体哪一张我忘了）后面写清楚的，你必须一直携带，而且警察有权让你出示。
但是实际操作中，大家都不把绿卡带身边的。也几乎很少有警察想到会要看你的绿卡，除非一些边关的警察等。你可以make a copy of your green card and take the copy with you. At least it has A# on it so if necessary, the police can check the A# in his computer --- that's better than having nothing to show them.