PCS has asked the Department for Work and Pensions for the statistical evidence behind the government's policy to limit access to social security for EU migrants.
PSC said the department claims it does not have the data.
However a former DWP chief economist has published departmental data that shows the proportion of those who make a claim within six months, proving the figures are available.
This raises serious questions about the integrity of DWP ministers who are refusing to publish the facts necessary to help inform public opinion, the union says.
PCS general secretary Mark Serwotka said: "We know this information is collected and that it will reveal the government is claiming to fix a problem that doesn't exist.
"The only conclusion to draw from the refusal not to publish the evidence is that the government is trying to hoodwink the public to appease a xenophobic but vocal minority on its backbenches."