There is no law requiring you to clean or re-paint between tenants, if that is what you are asking. The question is whether you can attract a new tenant at the price you want for rent with the place in the condition it is in right now. If prospective tenants seem unimpressed, a coat of paint and a clean carpet can make the place look shiny and new.
You are required to provide "reasonably secure locks" and a good way to be sure the locks are reasonably secure is to have a locksmith re-key the doors between tenants. This is also a great time to address maintenance issues; to look under the sinks and make sure nothing is leaking, to check the roof and the gutters to make sure all is well.
The only other reason I can think of to shampoo the carpets is to avoid any claim by new incoming tenants that there were fleas or bedbugs or something. Hope this helps.
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I would add that repainting (or doing a really top-notch touch-up job) and shampooing carpets between tenants is the best way to establish the baseline for the condition the unit needs to be in when the new tenant eventually vacates. Remember that you need to have a written move-in checklist describing the condition of the apartment in order to take a security deposit. Then, when the tenant vacates you have to provide a written explanation of why you have withheld any of the deposit, together with a refund of any remaining deposit, within 14 days after the tenant vacates. Essentially, the tenant's obligation is to return the apartment in as good condition as they received it, notwithstanding ordinary wear and tear. That means if the carpet was shampooed before they took possession, they need to return it in equally clean condition (again, subject to ordinary wear and tear). With that baseline standard established, you can create the most defensible position if it comes to a dispute over retention of some or all of the deposit.
Note that there are other statutory requirements when it comes to taking security deposits. I recommend that you check with an experienced attorney or your local landlord's association to ensure you understand your obligations before collecting a security deposit.
The foregoing is not intended as legal advice, but solely as general information. No attorney/client relationship exists between the poster and the answering attorney.