The largest upward contribution came from the recreation & culture sector where there were price rises for audio-visual equipment and books, newspapers & stationery.
While the largest downward contributions came from furniture & furnishings, motor fuels and meat.
The ONS said the CPI remained broadly flat through the second half of 2012 and into 2013 following a number of years of large increases and decreases.
Over the last six months the CPI 12-month rate has been particularly stable, standing at 2.7% for four months followed by 2.8% for February and March 2013.
CPIH, the new measure of consumer price inflation including owner occupiers' housing costs which is described as an experimental statistic, grew by 2.6% in the year to March 2013, also unchanged from February.
The slower growth in CPIH than CPI is due principally to owner occupiers' housing costs increasing more slowly than overall inflation for other consumer goods and services in the year to March.
Samuel Tombs, UK Economist at Capital Economics, said the headline rate is still likely to climb over the next few months probably to a peak of about 3.5%.
He said: “Recent rises in agricultural prices are likely to push up food inflation. And we are approaching the anniversary of a period of sharp discounting on the high street.”
But Tombs said, following today’s petrol price cuts and yesterday’s fall in oil prices, the inflation outlook looks brighter beyond the summer.
He said: “As a result we continue to think that inflation will fall quite sharply later this year and in 2014. So although inflation is likely to remain stronger than pay growth for another year or so, the end of the squeeze on real pay is at least in sight.”