Prince George's County may face difficult financial times in the fiscal year that begins next July because of smaller increases in state aid and demands for increased wages by county workers, according to a letter sent yesterday to the County Council by County Executive Lawrence Hogan. Hogan's letter states that the financial troubles that were widely anticipated last year because of the county's voter-approved tax freeze but averted because of massive infusions of state aid, may be unavoidable in the coming budget year, despite a surplus of $5 million that the Hogan administration hopes to raise to $14 million.

The state, Hogan wrote, is faced with its own financial problems and will probably not be able to provide any more money to Prince George's than it gave this year. The state aid, coupled with a $14 million surplus last year and small growth in the county's budget, allowed Hogan and the council to cut the county's property tax rate by 35.5 cents.

In addition, every labor contract in the county -- including that with the 9,000-member teachers union -- will expire on July 1, and cost-of-living demands are expected to be greater than the 5 percent increase given county workers this year. Hogan did not specify in his letter what cost-of-living increase he would be willing to provide county workers, except to say it would be "modest."

Also, Hogan wrote, the county's financial difficulties will be compounded if the council passes legislation it is currently considering, which would repeal the county transfer tax. That tax, which is paid by residents when they purchase a house, brings in about $11 million annually.

The council is due to consider the transfer tax repeal in the next few weeks and Hogan's letter and sketchy predictions of financial trouble in 1982 were designed in part to stave off passage of that legislation.

Supporters of the repeal on the council say that the transfer tax is an unfair burden, particularly on young people who would like to settle in the county and buy a home.