Mr Puchong said the first petition was filed by former Democrat MP Thaworn Senneam and related to the Feb 2 election.
Mr Thaworn alleged that actions taken by Ms Yingluck and Mr Chalerm might have been intended to benefit or disadvantage some political party or election candidates.
He said Ms Yingluck, as prime minister, set up the Centre for the Administration of Peace and Order (Capo) and appointed Mr Chalerm as Capo director. This allowed Mr Chalerm to issue orders to help the Pheu Thai Party gain popularity.
The EC dropped the petition on the grounds that their actions did not violate the election law, Mr Puchong said.
The other petition was filed by Leena Jang, a former Bangkok governor election candidate, against Khunying Jaruwan, who won the Senate election to represent Bangkok.
Mrs Leena claimed Khunying Jaruwan was not qualified to run in the election because while serving as auditor-general she was found by the National Anti-Corruption Commission (NACC) to have abused her authority under Section 157 of the Criminal Code.
Mr Puchong said the EC dropped the petition on the grounds that when Khunying Jaruwan applied to run in the election the Bangkok election committee asked the NACC about her qualifications and the anti-graft agency replied that she was qualified because the NACC's finding against her was not yet finalised.
The coup-makers later dissolved the Senate, making Khunying Jaruwan's tenure very short.
The EC also rejected another petition, which was not election-related, against former natural resources and environment minister Vichet Kasemthongsri.
The petition accused Mr Vichet of failing to notify the NACC of his wife's holding of more than 5% of the shares of a private company, which might be in violation of Section 269 of the constitution and Mr Vichet stood to lose his cabinet post as a result.
Mr Puchong said the EC received the petition on Oct 29 last year but could not consider it because its office was under siege by protesters. A committee set up to investigate it suggested the EC dismiss the petition because Mr Vichet was no longer a cabinet minister after the House of representatives was dissolved on Dec 9.