With the recent opening of a headquarters in an office being used by a state candidate, Democratic presidential candidate Michael Dukakis' campaign has established a base in Utah - again.

The newest headquarters is located at 250 W. Crossroads Square (2255 South), in an office and adjacent warehouse space already leased by Democratic candidate for state treasurer Art Monson.The Utah Dukakis for President Committee had opened a campaign headquarters at 543 E. Fifth South last April, before the state party chose its delegates to the national Democratic convention.

That headquarters only stayed open about three weeks before money from the national campaign and local sources ran out, said Pat Shea, co-chairman of the Utah Dukakis campaign.

Shea, who acknowledged that Utah is not a high priority with the national campaign, said the lack of a headquarters has not stopped Dukakis supporters in the state from meeting weekly since June 1987.

Money for the Crossroads Square headquarters came from the national Dukakis campaign as well as both the state and national Democratic party organizations, Shea said.

The campaign had hoped to rent space downtown to boost Dukakis' visibility among Utahns, but the price was too high and parking too difficult, said Pete Suazo, state campaign director for Dukakis.

Sharing space may also have more than a financial benefit for the Utah Dukakis campaign, which is also using space in Utah and Weber counties' Democratic headquarters.

Suazo said he expects the Democratic presidential candidate to benefit in Utah from the early lead Monson has taken against Republican incumbent Edward T. Alter.