How would I go about getting a police record on an person living in TelAvie, Isreal?

I think even if you lived there you couldn't do this yourself, you have to have permission to look at someone's police records or be in some type of law enforcement. Some private investogators (actually most) could use contacts to get police records however. Try finding a private investigator in Tel Aviv and see what they can do.

Now... why?

Check this site: http://www.police.gov.il/english/Information_Services/Criminal_Info/xx_criminal_info.asp

I do not think you will have much luck in accessing any information.