This leap day baby shares a birthday with her dad

(CNN) -- It's rare enough to be born on leap day. It's even rarer to share that leap day birthday with someone in your family.

And that's what makes Baby Camila's birthday special -- the little girl was born Saturday and has the same birthday as her father.

The staff at Mercy San Juan Medical Center in California took the opportunity to make a fuss of Camila. They dressed her up in a "leap frog" outfit and celebrated with a cake, balloons and a rendition of "Happy Birthday" for dad and daughter.

Her parents said they are thrilled at the connection.

"I prayed to God for my little baby girl and now we are going to share this amazing bond for the rest of our lives. I am just so happy!" gushed her father, Ivan Peñaloza.

Camila was due March 3, and her arrival surprised her mother.

"We feel so blessed to have our little Camila here and so incredibly shocked at the coincidence that she now shares her leap day birthday with her dad," Jennifer Rebollar Cortez said.

Even the hospital's president congratulated the family.

"Dignity Health Mercy San Juan Medical Center has a legacy of serving patients ... and we feel incredibly fortunate to share in this special, life-changing moment with this family," said Michael Korpiel, the hospital's president.

Officials with Dignity Health say babies born on this day are called "leapers."

One nurse at the medical center told CNN affiliate KCRA: "I've worked here 29 years I've never seen it happen. It's amazing."

The leap day is an extra day added every four years to the calendar to synchronize it with the solar year.

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