Thanks for your question.
Tennessee's "Peeping Tom" laws are found in Title 39, Chapter 13, part 6 of the Tennessee Code. The type of surveillance you are referring to would fall under either subsection 605, which pertains to unlawful photographing in violation of privacy:
or subsection 607, which pertains to observation without consent:
Basically, it is an offense to photograph/view a person where he/she has a reasonable expectation of privacy without first obtaining his/her prior effective consent, and also, the photography/viewing must not
1) offend or embarass an ordinary person if the person knew the person was being viewed, and
2) be for the purpose of sexual arousal or gratification of the defendant.
Also, if the person being viewed/photographed is a minor, the law is violated regardless of whether his/her parents' consent is first obtained.
I can foresee a lot of potential problems with installing video surveillance equipment in rental units. For instance, even though you may have obtained the tenant's consent to view/photograph him, each time a tenant has a guest in his/her rental unit, you will likewise have to obtain the consent of that guest before filming. And, if a minor child is involved, either living in the unit or visiting as a guest, you will never be able to film when that child is present due to the fact that a parent or guardian can never give consent for him/her to be filmed.
So basically, so long as you are in compliance with the law with respect to prior consent, you are not forbidden from installing cameras in rental units, but again, there are likely to be some problems.
Hope this helps.