How do you get closer to someone who has selective mutism? Seems very hard to do.

Patience. Yes, it can be difficult to develop a relationship with someone who has selective mutism. You have be ready to work on this over a long period of time. It will be important for the other person to see your interest and encouragement in him/her. You have to plan on the relationship developing slowly with the gradual building of trust.
Here is a reference. I have used this reference before and good luck: http://www.Amazon.Com/the-selective-mutism-treatment-guide/dp/9659178301/ref=sr_1_2?Ie=utf8&qid=1341509283&sr=8-2&keywords=selective+mutism.