Per IRS, you cannot if you prepared the 1120-H tax return.
"Electronic deposit requirement. Associations must use electronic funds transfers to make all federal tax deposits (such as deposits of employment, excise, and income tax). Generally, electronic funds transfers are made using the Electronic Federal Tax Payment System (EFTPS). However, if the association does not want to use EFTPS, it can arrange for its tax professional, financial institution, payroll service, or other trusted third party to make deposits on its behalf. Also, it may arrange for its financial institution to initiate a same-day tax payment (discussed below) on its behalf. EFTPS is a free service provided by the Department of the Treasury. Services provided by a tax professional, financial institution, payroll service, or other third party may have a fee.
Per IRS, you cannot if you prepared the 1120-H tax return.
"Electronic deposit requirement. Associations must use electronic funds transfers to make all federal tax deposits (such as deposits of employment, excise, and income tax). Generally, electronic funds transfers are made using the Electronic Federal Tax Payment System (EFTPS). However, if the association does not want to use EFTPS, it can arrange for its tax professional, financial institution, payroll service, or other trusted third party to make deposits on its behalf. Also, it may arrange for its financial institution to initiate a same-day tax payment (discussed below) on its behalf. EFTPS is a free service provided by the Department of the Treasury. Services provided by a tax professional, financial institution, payroll service, or other third party may have a fee.
Same answer -- refer to page 4 (left column, Electronic Deposit Requirement) of the official IRS 1120 instructions publication: https://www.irs.gov/pub/irs-pdf/i1120.pdf