Maryland residents registered in record numbers this year to vote in next month's general election, and in 10 of the heavily Democratic state's counties, more Republicans than Democrats registered during the last week before the Oct. 8 deadline, state and local officials said yesterday.

State elections administrator Willard Morris said that 2,253,141 Maryland residents are registered to vote, according to final figures released yesterday.

Nearly 68 percent of that total is Democratic, while Republicans account for just over 24 percent of the total.

State registration in 1980, the last presidential election year, was 2,038,000.

The last-minute push to register new voters showed a significant Republican Party surge, Morris said.

Of the 97,092 new voters who registered to vote between Oct. 1 and Oct. 8, state figures show that about 51 percent signed up as Democrats, but 33 percent -- or nearly 10 percent more than the state average -- listed themselves as Republican.

Another 15,560 voters, or 16 percent of the final eight-day total, registered but declined to affiliate with a party.

"Never has it ever hit that," said Morris, who has been state elections administrator since 1969.

In Montgomery County, where Democrats make up 208,349 of the 372,044 people registered and Republicans account for another 113,203, elections administrator Douglas Jernigan reported that between January and October, new Democratic registration accounted for 15.5 percent of the total, while Republicans made up 21.3 percent.

A whopping 30 percent of the new registrants declined to affiliate with either party in the county. Democrats held their own in the state's two most populous jurisdictions.

"That's what's got everybody guessing" about which party will benefit from the increased registration, Jernigan said.

But Democrats held their own in the state's two most populous jurisdictions. In Prince George's County, elections administrator Robert J. Antonetti Sr. reported that 304,564 people are eligible to vote Nov. 6.

Of that number, 210,703 are registered Democrats and 62,934 are affiliated with the Republican Party.

In 1980, about 265,000 county residents registered to vote.

In Baltimore, elections officials reported a record 439,925 city residents have registered to vote -- breaking the old record of 431,000 set in 1970.

Of this year's total, 383,308 are Democrats, 36,780 are Republicans and another 19,380 did not choose a party affiliation.

Even with those heavily Democratic registration figures, some local Democrats in both jurisdictions have expressed concern recently that their area could join a Maryland tide of support for President Reagan on election day. Despite the Democratic edge in registration, recent polls have shown Reagan leading in the state.

Howard elections administrator Barbara Feaga said that of 77,670 residents registered this year, 45,044 are Democrats and 23,025 are Republicans.

In 1980, 65,395 Howard residents were registered to vote.

Anne Arundel elections chief Betty Eby said there was a nearly 20,000-voter increase on this year's books.

Overall, 177,019 persons are eligible to vote in Anne Arundel, 109,545 of whom are registered Democrats and 53,549, Republicans.

In 1980, 158,163 Anne Arundel County residents registered to vote.

The Republican Party showed particular registration strength by outnumbering Democratic registrants during the final days in Anne Arundel, Frederick, Harford, Calvert, St. Mary's, Carroll, Washington, Garrett, Cecil and Allegany counties.