U.S. job openings fell in March, signaling a possible slowing in labor demand, according to data released Tuesday by the U.S. Department of Labor.

Available positions fell to 3.8 million during March, just below February's revised reading of 3.9 million. The Labor Department's monthly Job Openings and Labor Turnover survey also showed that the hiring rate slipped to 3.2 percent from 3.3 percent.

The so-called quits rate inched downward to 1.6 percent from 1.7 percent the prior month, a possible sign that people are too worried about their next job prospects to leave their current position.