Short answer. No. Under Article 12(4) of the Revised Penal Code, a person is exempt from criminal liability when, while performing a lawful act with due care, he causes an injury by mere accident, without fault or intention of causing it. If those elements truly hold, no crime is committed.
What the law says
Any person who, while performing a lawful act with due care, causes an injury by mere accident without fault or intention of causing it
Revised Penal Code, Article 12 — Exempting Circumstances: Insanity, Accident And Minority. Read the full provision →
The accident exemption
Article 12 lists circumstances that exempt a person from criminal liability, and the fourth fits your question exactly: Any person who, while performing a lawful act with due care, causes an injury by mere accident without fault or intention of causing it. When this applies, the law treats the harm as a genuine accident, not a crime. The person is not punished because the act itself was lawful and carefully done, and the injury was neither intended nor the product of negligence. It is a true misfortune, and misfortune without fault is not a felony.
The four things that must all be true
The exemption is narrow because every element must hold together. First, you must have been doing a lawful act — not something already forbidden. Second, you must have exercised due care; carelessness defeats the defense. Third, the injury must result from mere accident. Fourth, there must be no fault or intention of causing it. If any one fails — if the act was unlawful, or you were reckless, or you actually meant harm — this exemption does not apply, and your conduct may be judged under the ordinary rules on intentional felonies or criminal negligence instead.
Accident versus negligence
This is the line that most often decides real cases. An exempting accident assumes due care; a person who causes injury through imprudence or negligence is in a different category and may be liable for a culpable felony. The presence or absence of care is therefore central. Because the accused is the one invoking the exemption, he generally carries the burden of showing that he was performing a lawful act, with due care, and that the injury was purely accidental. Bare assertion that "it was an accident" is not enough; the surrounding facts must bear it out.
A caution on the rest of Article 12
Article 12 covers more than accident — it also deals with insanity and, in its paragraphs on age, with children. Be aware that the age thresholds printed in this article no longer state current law: Republic Act No. 9344 (2006), as amended by Republic Act No. 10630 (2013), now governs the criminal responsibility of children and routes an exempt child through intervention or diversion rather than prosecution. For your accident question, though, the fourth paragraph is what applies, and it turns entirely on lawful act, due care, and absence of fault or intent.