President Carter has come from far behind and passed Ronald Reagan in the past month, whether or not independent John Anderson is included in the survey, according to a CBS-New York Times poll released yesterday.

The poll, which was completed Sunday, showed Carter with 38 percent to Reagan's 35 and Anderson's 14. A return to the Democratic fold by supporters of Sen. Edward Kenney was cited as one factor in the change. Another was a belief among two-thirds of those polled, includng Republicans, that Reagan "is-careless about what he says."

Meanwhile, a Republican Party poll showed Reagan and Carter neck and neck, with Anderson trailing and a marked increase in the last two weeks in the number of undecided voters at Reagan's expense.

Robert Teeter, whose firm conducted the poll, declined to give the exact figures on presidential standings. But he said the undecided vote has grown from 13 percent in June to 18 percent, compared with a 9 percent norm for this point in an election year.

Despite the falloff in Reagan support, the Teeter poll indicated that the Republican Party's $8 million TV ad campaign has improved its image, that being a Republican is no longer a "millstone," but is "at least a neutral" for congressional candidates.

A new Gallup Poll, meanwhile, showed that voter support for Carter, after rising sharply after the Democratic convention, has leveled off. The poll showed the Carter-Mondale ticket with the support of 38 percent of registered voters and the Reagan-Bush slate with 40 percent. The independent ticket of Anderson and Patrick Lucey receives 15 percent.

The survey was conducted last weekend, during a period of widespread discussion of the president's refusal to join Reagan and Anderson in the debate scheduled Sunday in Baltimore.