LONDON — Swiss prosecutors said on Wednesday they had opened a criminal investigation into a tax case involving the French luxury group Kering, widening the legal scrutiny of its tax practices in Europe.

The announcement comes four months after Italian authorities began looking into Kering’s flagship brand, Gucci.

The Swiss attorney general’s office said that it had “received and acted upon” a request for assistance by the public prosecutor’s office in Milan. The Italian inquiry, which began in November and is being led by a national police force specializing in financial crimes, included a raid on Gucci offices in Florence and Milan.

At issue in the Italian case was whether profits Kering made on Gucci sales in Italy had in fact been declared in Switzerland, where tax laws are more favorable. The Italian newspaper La Stampa reported last year that the authorities were looking into whether Gucci should have paid as much as 1.3 billion euros, or $1.54 billion, in past domestic taxes.