Sydney police laid the charges following an investigation and subsequent arrest of a man on Sunday.

At about 1.10pm on January 21, a 64-year-old woman and a seven-year-old girl boarded a regional passenger train at Wagga Railway Station, travelling to Sydney.

"While on the train, the woman and girl were approached by an unknown man who began speaking with them," a NSW Police statement said.

"The man then allegedly sexually touched the girl, before leaving the carriage.

"The incident was reported to police when the woman and girl arrived at Central Railway Station."

Officers attached to Sydney City Police Area Command subsequently commenced an investigation.

Following extensive inquiries, a 55-year-old man was arrested at George Street, Haymarket about 4.10pm on Sunday.

"In a search of the man, officers located fraudulent identification documents, which were seized for forensic examination," police said.

"The man was taken to Day Street Police Station and charged with intentionally sexually touch child under 10 years, procure child under 14 years for unlawful sexual activity, and three counts of goods in personal custody suspected being stolen (not motor vehicle).

"The man, from Haymarket, was refused bail to appear in Central Local Court."