TUESDAY APRIL 03, 2007 08:00 AM EDT

Former Spice Girl Melanie Brown welcomed a baby girl early Tuesday, PEOPLE has confirmed.

"The baby is completely healthy with a good head of hair," a rep for Brown said in a statement.

"Mother and baby are now resting. No name has been decided on as yet and she is purely known as Baby Brown."

Brown, 31, was taken to Saint John's Hospital in Santa Monica at around 5.30 p.m. Monday and the baby was born just after midnight Tuesday, the rep said.

The new arrival – who weighed in at 5 lb., 4 oz. – joins 8-year-old sister Phoenix Chi, Brown's daughter with ex-husband Jimmy Gulzar.

The paternity of the new baby, however, is in question. Brown has said her ex-boyfriend, Eddie Murphy – who shares a birthday with the infant and turned 46 on Tuesday – is the father, but he has questioned that claim.

"I don't know whose child that is until it comes out and has a blood test," Murphy said on a Dutch TV show in December when asked about impending fatherhood. "You shouldn't jump to conclusions, sir."

Brown later released a statement saying she was "upset and distressed" by Murphy's comments.

In March, Murphy's new girlfriend, film producer Tracey Edmonds, told Chicago's Power 92 radio station of Murphy and Brown: "Without me getting too deep into it, they had a quick relationship before I even got into that, before I got into a relationship with Eddie. So that's like their business that's going on. There'll be a paternity test and if it's his then he'll be responsible."