One of the great distinctives of Baptist churches is that we are a group of autonomous churches, meaning every church has the authority and responsibility to govern themselves. I hold to local church autonomy because I think it is taught in Scripture. No one should be a part of a Baptist church if they do not hold to local church autonomy. And no one should hold to local church autonomy if they do not think it is in the Bible. I cannot tell you how many Baptists I have met, including pastors, who like local church autonomy but are not Scripturally convicted about it. I can tell you what that amounts to: many Baptists just do not want anyone outside their local church telling them what to do or what to believe. I think that is a terrible reason to be Baptist.
One place I see local church autonomy taught in the Bible is Matthew 18.15-20. Jesus commands his disciples to carry out church discipline in matters of sin. If a professing believer sins, and then does not listen to you, or to you and one or two others, then you take the matter before the church. If that person refuses to listen to the whole church, then you treat them like an unbeliever. Now there are debates about how to interpret and apply that, but one sensible interpretation is that the “church” in that passage is the local church. And it is the whole church that has the final authority in church discipline matters. In other words, no outside body has any say in your church’s discipline issues. It is the local church’s autonomy that is in view in Matthew 18.
I would say local church autonomy is an implication of that text. But depending on how you understand it, it is a necessary implication. And the necessary implications of the text are as authoritative as the explicit statements. So in studying Scripture, look for the explicit theology, commands, and prohibitions, but also the implicit teachings as well. And do know why you believe what you believe from the Bible.