Apple (AAPL), Google (GOOG) and Research in Motion (RIMM) have reached something like a three-way stalemate in the battle for dominance of the U.S. smartphone market, according to Nielsen survey results scheduled for release Tuesday.

Smartphones are increasingly popular — they now represent 37% of all U.S. mobile phones — and smartphones running Google’s Android operating system are the most popular of all. But Android’s slice of the pie was no bigger in April than the last time Nielsen surveyed the field.

After having raced to the No. 1 spot in less than a year — climbing from a 15% share in June 2010 to 37% in March 2011 — Google held steady at 36% in the three month period from Feb. to April 2011.

Apple also held steady. Its market share over the past three months weighed in at 26% — within a few points of where it’s been in Nielsen’s surveys for more than a year.

Even RIM’s BlackBerry may have started to slow its long decine, settling in at 22% to 23%.

The one surprise in Nielsen’s report for April was how data-hungry Android users turn out to be.

Although iPhone owners are more likely than Android aficionados to download apps, stream music or watch videos, individual Android users who do that kind of stuff tend to gobble up significantly more data. A Nielsen analysis of nearly 65,000 cellphone bills in the U.S. found Android owners consuming an average of 582 MB of data each month, compared with 492 MB for iPhone owners. See charts below: