The girls, aged 11 and 12, were playing at the grandstand at Arpentuer Park on Arpentuer Drive on Tuesday at the time of the assault.
About 11.50am a man with a small, scraggy, grey-haired dog approached the girls and engaged them in conversation before he indecently dealt with them.
He left on foot.
The man is described as being in his 30s with fair skin and a medium build.
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READ NOWHe was wearing shorts, a T-shirt and a cap.
Detectives would like to speak to anyone at the park between 11.30am and 12.30pm who may have seen the incident or the man.
Call Crime Stoppers on 1800 333 000 or make a report at www.crimestopperswa.|com.au.