For general scanning, I'd just go with a regular cable TV splitter. I have done this before, and I know, I know those splitters ARE somewhat lossy in terms of RF, but, I was still able to scan about 40 miles with it.
Your major limitation is going to be the antenna. Don't worry about the splitter. I know someone will jump in here and say they work like crap, but hey, take it from me, Me and a fellow ham buddy of mine, had two identical scanners. RadioShack 2051's actually. We split both scanners into one scantenna, and was recieving Iowa Police in Kentucky one night when skip was high.
There are "real" splitters out there for scanners that will let you connect one scanner to multiple antennae, or multiple scanners to one antenna. They're around 100 bucks I think. Go spend 5 for a basic Cable TV splitter. Like said, your performance won't be awesome, but it WILL work decent.
Why would you want to turn your TV off in order to listen to the scanner? If you have a splitter, splitting the TV antenna between your TV and your scanner, you wouldn't have to turn the scanner off to watch TV, or turn the TV off to listen to the scanner. Both recieve only. I have 3 scanners hooked to one antenna, and all three run constantly.
Now if the TV somehow could transmit, then it wouldn't be a good idea. But in a recieve only situation, hook anything you want to one antenna and you should be fine.
On another note, TV booster boxes, make good scanner amplifiers. TV band runs in the 800 mhz range I belive, or is it 400? I dunno, but still, if you hook a TV booster to your scanner, you'll REALLY suck in the stuff around the TV band. If it operates in the 800 range, you'll rock on trunked frequencies, if it's 400, UHF will roar as well. But, be ready to deal with consequences of an amplifier. Not only will you amplify signals, but you'll also amplify NOISE... That's right.. your noise level will rise as well.
Enjoy..