Er lief beim Anblick einer Polizeistreife davon.

English Translation

He ran away at the sight of a police patrol.

In this context I think it is more likely “er rannte…”

Yes, “davonlaufen” leaves it open whether someone ran or walked.

Since it’s mentioned here that he “ran”, you can definitely say “Er rannte … davon.”

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Wiktionary (laufen - Wiktionary, the free dictionary) says:

to walk; to jog; to run (to move on foot; either at a normal or an increased speed)

So it’s not restricted to slow walking.

But yes, “rannte” also works.

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