How to write a apartment manager complaint letter about sink clogged problem?

Here is a possible

make it look officialish SEND IT REGISTERED MAIL, RETURN RECEIPT REQUESTED that means they have to sign for it and you have legal proof of delivery. They will send you a card saying it was signed for. Save that and a copy of the letter. Very lawyer like. It will scare them and your sink will be fixed asap. I do it all the time.

On nice paper typed
centered --your name, address, phone, email
down two spaces
centered--date

down two spaces
apt manager's name
address
city

Re: Clogged sink in apartment __ at (address)

Dear ________,

I am the tenant in apartment ___. I have a maintenance problem in that the (kitchen, bathroom) sink drain is clogged and will not drain.

I have made the following efforts to unclog the sink: (list attempts to unclog) and contacted the apartment management about said maintenance problem on these occasions (list dates and who you talked to).

The sink poses a health issue because the stagnant water is a breeding ground for bacteria and insects. It diminishes my enjoyment of the premises because of the unpleasant odor.

In accordance with our lease, management is responsible for this kind of maintenance: (quote what lease says).

Also quote anything in the lease forbidding you from doing the repair.

Please have the sink unclogged as soon as possible per our lease.

Sincerely,
your name

Certified mail
return receipt requested
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When writing the letter the best thing you want to do is to make sure you have everything you have done to resolve the situation in the past documented.

Generally a letter is because the manager did not respond to your first requests. Send the letter certified mail. This is generally enough to shake up even the most dense property manager into realizing it's about to get worse if he doesn't make it better.

Good luck, and hope this helps
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first talk to them, then you can either send an email or put it in letter format, if you know who it is specifically going to, then write dear mr so and so or to whom ever it may concern. In the body of the question write, I am writing this as an immediate need to have my sink unclogged, mention how it is a hazard and is contributing to many other problems, be as detailed and as mild as possible, try not to make your wording inflammatory
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I am guessing that they require written request for repairs.
If this is the case it does not need to be formal or certified or mailed . All you need to do is write down what your service request is and sign it, make a copy, and give it to the manager.
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Just write that your sink is clogged through no fault of your own negligence and you are requesting a repair.

If you cause the clog, be prepared to pay for the repair.
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simple just write the letter expressing your concerns of the clogged sink or if you have the managers number you could just call him and tell him
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It does not have to be complicated.

Just a simple "this is the problem" kind of thing would be fine.
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Have you tried a plunger?