As far as I know,  there are no car downloads that have a built in siren.  This is not possible!

The car you download may have a siren file inside.  But those have to be separately and manually installed by you.  Installing a car should do nothing to the siren ingame.  The video should shed some light on it for you.

And I'm pretty sure you can only have ONE siren model.  It is contained within one file that all the vehicles use "HORNS.ivaud".  And the format of that file is very strict on the length of audio/tones and limits what you can do with it.  (someone correct me if I'm wrong)

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Ok yeah, I got confused because I guess what it is, is that some cars come with a file you are supposed to copy over to the slot control folder. I guess it does certain things but not a siren. But thats my question, how do I activate those type of files? Here is an example of one that came with a car I downloaded.

 police.ini

Good news NoleBlooded.  

https://www.youtube.com/watch?v=EbGXF4bv_SQ

  A video tutorial on it.  Old video but the info still applies.   Way better than anything I could type out to help you.  If you want to cut to the chase,  start watching at the 4:45m mark for answers to your last question.

Jeff has a solid tutorial playlist on modding and commonly used mods.  Check the whole thing out if you have time. 

https://www.youtube.com/playlist?list=PLo5whi14bKminUvTpNfwuidJ1Atjpme8B