Washington Gas Light Co.'s 150,000 District of Columbia customers will begin receiving small refunds on their gas bills starting with this month's bills because the company overcharged customers last year. This much is known.

It is less clear who is going to get the credit in the public mind for bringing this about. Both WGL and the D.C. Public Service Commission, which regulates utility rates, seem to be claiming the honor. Here is what happened:

Just before the close of business yesterday, the PSC sent out a news release saying it would "investigate" WGL's purchased gas adjustment charges to customers -- the portion of monthly gas bills in which the company passes through certain special costs it incurs in buying gas.

The release said WGL appears to have "overcollected" $1.6 million from customers through that mechanism last winter, adding that, "WGL has been directed to commence the refund of the overcollection beginning with the December 11, 1978 billing period."

The release went on to say that, "The causes of the overcharges are not known at this time and their determination is the purpose for which the PSC has instituted this investigation."

"I'm just a little surprised," said WGL spokesman Paul Young when asked about the news. "This is a procedure that we initiated a year ago and it was approved by the commission and we have already taken steps for a refund starting with the December bills."

Young said WGL "initiated" the refunds by arguing in favor of them before the commission.

Assistant D.C. People's Counsel Elizabeth Noel, who represents consumers in utility cases, said she had not seen the news release yesterday and did not know what the furor was all about.

In any case, the refund will amount to a total of $8.20 for heating customers and $1.52 for non-heating customers -- paid back on bills in 12 installments. Customers will not be able to see the refund as a separate item on their bills, according to the gas company, since it will be folded into the gas adjustment portion of the bill as an unseen credit.