Assume nothing. Make sure you have the right to push the record button. Rights to record, copy, make CDs of, or broadcast the work of others are covered by copyright laws. In most cases, the basic CCLI licenses that most churches have do NOT cover broadcast. Even putting a video of the service on the church website can be a violation of these laws if it contains music or material created by others. There isn't an issue with a sermon or teaching since the pastor or teacher owns the rights to their own material. But, we become so familiar with songs that we sing in every service we may forget that it was written by someone who holds the copyright on its use.
Find out what the laws are and how they apply to your situation. You could start with a visit to www.CCLI.com. The link to the specific question of what can be broadcast can be found by going to the “50 most asked questions” section: http://support.ccli.com/knowledgebase/afmmain.aspx?topicid=&faqid=&question, Type: ‘BROADCAST' in the search bar. Another great site for information is www.copyrightsolver.com/, which is hosted by the Church Copyright Administration (CCA).
"First Things First! Know Copyright Law to Protect Your Church" is an online-only side-bar article to "Audio Mixing: Broadcast vs Live" by Mark Johnson, found in the March 2010 issue of Church Production Magazine.
