You'd be better off buying a commercially manufactured splitter from one of several sources. Dig through the threads in the scanner antenna forums, it's a popular topic of discussion.
A splitter you buy off the shelf is likely to have all BNC connectors on it, although other choices are available. So, your cabling just has a BNC connector on the splitter end, and the appropriate connector for whatever it's hooked to on the other end.
A passive splitter will have a significant amount of loss, so you may want to look into either active splitters, or a separate preamp to insert in the line between the splitter and the antenna. But that opens up a whole big can of worms to watch out for.
Look through the threads here for ideas:
Passive Devices - The RadioReference.com Forums