Is there any statistical relation between date of birth and date of death. Could it be within three months?

You clearly mean not to consider the year in your date comparison, or you are suggesting that all people die at three months of age. Yes, your birth and death month and day could be within three months. They also can be as far apart as 6 months. They can be anywhere from 0 days to about 183 days apart. It is very unlikely that you will find any kind of unbiased, systematic relationship other than simple chance. Now if you think about how far from your birth month and day your death month and day can be, and if you crunch some numbers, you will probably find that the average distance is 3 months. This should not be surprising at all. But does it have any meaning? The 'distribution of birth/death difference' will not be a normal curve with 3 months at its center.