Prince George's County Executive Parris Glendening, who has had trouble persuading the legislature to bail his county out of its financial troubles, ran into more skepticism today. One state delegate told him one of his key tax measures should be taken back to the County Council and another challenged his dire budget figures.

In the meantime, Democratic Del. Charles J. Ryan, chairman of the county delegation, has dispatched a University of Maryland economist to take a look at the county's budget records. Ryan, who is expected to get a written report on the review next week, said yesterday he wanted an "independent assessment" of the budget figures.

All of this comes amid growing friction between Glendening and the county's legislators, who have complained that the executive has not consulted with them enough, a point that Glendening disputes.

Prince George's officials, faced with what they now say will be a $35 million budget shortfall, have asked the legislature to approve a bill that would grant the county authority to increase the personal property tax to raise $10 million more in revenue. Two-thirds of that increase would come from taxes on business properties in the county owned by major utility companies.

But today, Del. Timothy F. Maloney (D-Prince George's) released a letter from the Maryland attorney general's office that said the new bill is not only unnecessary but would violate the county's home rule authority to set its own tax rates.

The attorney general's office told Maloney that the county already has the power to increase the personal property tax rate. Authority to increase that tax rate is important to the county since a voter-approved measure known as TRIM froze the amount of real estate tax money that could be collected from homeowners at $142 million, the 1979 level, while inflation has pushed up the cost of county government.

Glendening said today he would be reluctant to ask county legislators to withdraw the tax bill until he and his staff are "absolutely certain" that the attorney's general's advice is valid.

Other sources in the county government expressed concern about legal battles that could break out if the tax is imposed by local action but later overturned if the courts determine that action by the state legislature in fact was required.

In another development, Del. David Bird (D-Prince George's) said Glendening is making his budget problems out to be worse than they really are by underestimating the county's available revenues for the next fiscal year by more than $18 million.

Bird, coauthor of the TRIM amendment, said computations by one of his aides showed that the county had been overly conservative in figuring money available from taxes, state revenue shared with the county and in estimating its budget surplus.

Glendening said he would take a look at Bird's projections.

Another part of Glendening's tax package had an easier time with the delegation today. A proposal to increase the local surcharge on the state income tax from 50 to 60 percent of the amount paid to the state, was accepted for hearing by the county delegation. The bill, which was introduced after the normal cutoff date, was sent to a delegation committee for public hearing.