There are two main sources for this statistic. The first is a 1991 hearing before the Select Committee on Children, Youth, and Families in the House of Representatives. The full report, “On the Front Lines: Police Stress and Family Well-Being,” can be found here.
This is from the statement given by Dr. Leanor Boulin Johnson, Associate Professor of Family Studies at Arizona State University, when describing the results of her research:
“Family violence seems to be a problem as well. Some argued that officers who work daily in predominantly negative and sometimes violent environments may unconsciously promote and perpetuate acceptance of violence in their own lives.
We found that 10 percent of the spouses said they were physically abused by their mates at least once during the last six months prior to our survey. Another 10 percent said that their children were physically abused by their mate in the same last six months.
How these figures compare to the national average is unclear. However, regardless of national data, it is disturbing to note that 40 percent of the officers stated that in the last six months prior to the survey they had gotten out of control and behaved violently against their spouse and children.”
The second source is a study published in 1992 in the journal Police Studies entitled “Interspousal aggression in law enforcement families.” The full article is locked behind a paywall, but you can see the first page (including the abstract) here. The abstract also contains the 40% figure (a very slight rounding down of the number found in the actual study, which was 41%). The Fraternal Order of Police found this study important enough that they reprinted it in their own journal later that year.
The reason these studies came to be so widely cited is that both were based on self-reports. Since not all domestic abuse is reported, and since people are likely to downplay the frequency of their own negative behavior, the fact that 40% of officers were willing to admit to committing domestic violence during the past year was considered a big deal. The reason that these numbers continue to be so widely cited is that increasing stigmatization of domestic violence has made it harder to conduct studies like these.
That said, we should bear in mind that (1) these studies are now three decades old, (2) neither was a national study (as Dr. Johnson notes in her testimony), and (3) it is almost impossible to obtain internal data from police departments regarding how often officers are reported and/or investigated for domestic violence (which could potentially give us a broader understanding of the situation and help us fill some gaps in the existing studies).
One last note about methodology: surveys are—or at least can be—a very important part of a study. So while both of these studies used surveys to gather their primary data, neither just stopped there. The data was analyzed using well-tested statistical tools before it was reported.