The answer depends on the age of the child. It is possible, before age 1, in some cases, to correct a birth certificate directly with vital records. After that, you need a lawyer, and will need either to have him file a legitimization (he has to file that), or perhaps you could do a petition to correct the birth certificate (the former option being better than the latter).
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As my colleague said in his answer, depends on the age of the child. As the mother, you can consent to the legitimation, at which point the judge, upon proper filing, can approve the petition to legitimize. However, it is possible for the judge to mandate a paternity test. It could be an easy process for you, or it could get complicated. You should consult an attorney to guide you through the process.