I have never heard of a court having form paper work to fill out to accomplish what you describe. However, neither I nor any other lawyer has practiced everywhere, so perhaps there is such a form somewhere.
The vast majority of folks choose to lay out fines and costs of court if they cannot pay. However, there is an obscure area of constitutional law that supports the idea that a person who cannot - as a matter of actual fact - pay, should be allowed time to make payments. And, some courts have community service programs to work off fines and costs without jail.
Criminal defense lawyers rarely charge for the first visit. For that reason, may I suggest if this is an actual problem that you are facing, that you schedule a brief visit with a ticket defense lawyer where the problem is going on in order to receive actual legal advice specific to the situation.
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It is up to the individual municipal court. Go to the court and ask the clerks if they have such a policy and how it works.
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