Is congregational approval required to lease part of our building?

Jim,

I would recommend it.  According to the 2008 Manual of Church Government (may be a more recent one, this is the only one I have) "In matters pertaining to certain items of facilities, other capital assets, and salaries, the council is required to seek the judgment of the congregation.  As a corporate entity the council serves as the board of trustees of the congregation."  Hopefully that answers your question.

Jim, I agree with Jeff basically.  However, it might depend on policies that the church already has in place.   If you have policies relating to public use of the facilities under certain conditions, and if the antenna does not significantly alter the ambience or spiritual atmosphere of the building, a council might take it upon themselves to make a decision without having a formal congregational meeting.  Sometimes a simple yes/no ballot vote after a church service may be sufficient, or an announcement with opportunities for individuals to raise objections to council could suffice. 

Although it's not related to congregational approval, I just wanted to make sure that you saw the article Sheri has linked on this page (it's called "Cell Tower Leases - Do's and Don'ts for Churches"). Seems like a great resource.

However the decision is made, be careful.  The church may be exposed to discrimination charges if you rent or lease to some, but refuse to do so to others, on the basis of doctrine.